algebra 2 assignment simplify

Infinite Algebra 2

Test and worksheet generator for algebra 2.

Infinite Algebra 2 covers all typical Algebra 2 material, beginning with a few major Algebra 1 concepts and going through trigonometry. There are over 125 topics in all, from multi-step equations to trigonometric identities. Suitable for any class with advanced algebra content. Designed for all levels of learners, from remedial to advanced.

Included in version 2.80.01 released 7/12/2024:

• Fixed: [Windows] - Superfluous log files created under certain conditions

Included in version 2.80 released 6/12/2024:

• Improved: Faster, more reliable backend
• Improved: Licensee name displayed
• Improved: Use HTTPS for all links
• Fixed: Rational Exponents > Rewriting in Radical Form - Index linked to wrong settings
• Fixed: Systems of Equations Word Problems - Typo

Included in version 2.70.06 released 1/5/2023:

• Fixed: Choices could appear incorrectly

Included in version 2.70.05 released 12/21/2022:

• Fixed: Continuous Exponential Growth and Decay Word Problems - Could generate an incorrect answer

Included in version 2.70 released 7/8/2022:

• New: Add preferences for Metric/Imperial units
• New: Add preference to “Prefer x“ as the variable letter
• New topic: Discrete Relations
• New topic: Continuous Relations
• New topic: Evaluating and Graphing Functions
• New topic: Direct and Inverse Variation
• New topic: Continuous Exponential Growth and Decay
• Improved: UI, security, and stability with updated libraries
• Fixed: Properties of Exponents – Choices could be equivalent
• Fixed: Properties of Logarithms – Choices could be equivalent
• Fixed: Solving Exponential Equations With Logarithms – Choices could be equivalent
• Fixed: Geometric Series – Choices could be equivalent

Included in version 2.62 released 2/8/2022:

• New: Print questions from Presentation View
• New Topic: Discrete Exponential Growth and Decay Word Problems
• Improved: UI, security, and stability with updated framework and libraries
• Improved: [Mac] Dark mode
• Fixed: [Windows] - Detached topic list does not close when application is closed
• Fixed: Probability Mutually Exclusive Word Problems - mutually exclusive case given when inappropriate

Included in version 2.61.03 released 9/10/2021:

• Improved: Minor UI improvements
• Fixed: Law of Cosines - Crash when opening topic
• Fixed: [Windows] Unable to change page layout to landscape
• Fixed: [Windows] Error 'Unable to load platform plugin'

Included in version 2.61 released 8/27/2021:

• Fixed: Preferences page for Kuta Works
• Improved: Security and stability with updated networking libraries

Included in version 2.60 released 8/19/2021:

• Improved: Site licenses check expiration date more frequently
• Fixed: Combinatoric Word Problems - Values could overflow
• Fixed: Properties of Exponents - Answer might not be fully simplified
• Fixed: Properties of Logs - Possible to have duplicate choices
• Fixed: Radical Equations - Option to mix radicals and rational exponents had no effect

Included in version 2.52 released 6/14/2019:

• New: Scramble questions by directions
• New: Scramble all questions in assignment
• New: Consolidate question sets with identical options
• New: Regroup question sets by directions
• New: Kuta Works - Create a two semester course
• New: Kuta Works - Clone assignments from a previous course into a new one
• Fixed: Presentation View - Arrow keys could change zoom at start/end of assignment
• Fixed: Tight Layout - Directions could be cramped for no reason
• Fixed: Inverse Trig - Angles limited for tan( x )
• Fixed: Inverse Trig - Errors in UI logic

Included in version 2.50 released 4/12/2019:

• New: Kuta Works - Option to hide answers and results from students until after due date
• New: Kuta Works - Option to control how long choices are hidden
• Improved: Options windows appear at a better initial size
• Improved: Window controls shown at their native size and spacing
• Improved: Network proxy configuration window
• Improved: License activation process
• Fixed: Presentation View - Answers could be cut off
• Fixed: Some window controls cut off on Windows 10 with display scaling
• Fixed: Spelling errors
• Fixed: Kuta Works - Course list could display more than just your active courses
• Fixed: Graphing Rational Functions - Open holes in graph could appear as filled holes

Included in version 2.42 released 12/11/2018:

• Fixed: Certain symbols incorrect if saved on Mac and loaded on Windows or vice versa
• Fixed: General Sequences - Recursive formula sometimes wrong
• Fixed: Properties of Logarithms - Avoid questions with reducible roots

Included in version 2.41 released 9/26/2018:

• Fixed: Archived courses in Kuta Works are now hidden
• Fixed: Generating or regenerating questions could cause a crash

Included in version 2.40 released 8/8/2018:

• New: Integrated with Kuta Works . Now post assignments online.

Included in version 2.25 released 4/27/2018:

• Improved: Generate questions more quickly
• Improved: Measurement arrows reach correct endpoints
• Improved: Absolute Value Equations - Better decimal numbers
• Improved: Absolute Value Inequalities - Better decimal numbers
• Improved: Compound Inequalities - Better decimal numbers
• Improved: Multi-Step Equations - Better decimal numbers and more predictable special cases
• Improved: Multi-Step Inequalities - Better decimal numbers
• Improved: Order of Operations - Better decimal numbers
• Fixed: Trig units for piecewise functions and ordered pairs
• Fixed: Graphing Rational Functions - Prevent equivalent choices
• Fixed: Law of Sines - Program could freeze
• Fixed: Transformations - Prevent equivalent choices

Included in version 2.18 released 7/31/2017:

• Fixed: Open circles on graphs were filled in when displayed as answer in red
• Fixed: Typo in sample custom question
• Fixed: Transformations - Program could freeze
• Fixed: Systems of Quadratic Equations - Program could freeze

Included in version 2.17 released 4/27/2017:

• Improved: [Windows] "Export to clipboard as bitmap" renders image with better quality
• Fixed: Probability with Combinations and Permutations - Could ask about impossible lottery ball

Included in version 2.16.20 released 11/16/2016:

• Fixed: Solving Quadratic Equations by Taking Square Roots - Option to "Allow fractions" not working as expected

Included in version 2.16 released 9/16/2016:

• Fixed: Numbers with many significant digits could round incorrectly
• Fixed: Customized question containing an error could not be modified
• Fixed: Customized question containing an error could cause a crash
• Fixed: Feedback tool detects Windows 10 properly
• Fixed: Mouse cursor when drag-dropping a question
• Fixed: Keyboard shortcut for changing order of question sets in assignment

Included in version 2.15 released 7/14/2016:

• Improved: Reorder question sets by dragging and dropping
• Improved: Move individual questions within a set by dragging and dropping
• Improved: Presentation View - Commands now on a movable, dockable toolbar
• Improved: Added option for large toolbar icons
• Improved: New icons
• Fixed: Certain options could result in double parenthesis or parenthesis around a negative sign
• Fixed: Arrow over vector variable name not red when appropriate
• Fixed: Solving Systems of Equations by Graphing - Answer could be displayed twice
• Fixed: Equations of Parabolas - Certain givens indicate wrong sign

Included in version 2.11 released 5/13/2016:

• Improved: [Windows] "Export to clipboard as bitmap" pastes into Microsoft Word at appropriate DPI
• Fixed: Keyboard shortcut for adding space to question set

Included in version 2.10 released 5/11/2016:

• New: Preference for including "None of the above" as a choice
• New: One column layout
• New: Added support for Infinite Precalculus
• New: Easily add piecewise functions of graphs in custom questions: Example: piecewise([2x-3] if [x<5], [x-1] if [x >= 5])
• New: Easily add functions with restricted domains to graphs in custom questions Example: function(x/2, x<0)
• Improved: More efficient layout of choices
• Improved: [Mac] Added option for legal paper in page setup
• Fixed: Spelling and grammatical errors
• Fixed: Graphing Quadratic Functions - Prevent equivalent choices
• Fixed: Binomial Theorem - Certain options didn't allow for many questions
• Fixed: Right Triangle Trig - Couldn't select just one ratio except sine
• Fixed: Right Triangle Trig - Answer sometimes given in problem
• Fixed: Law of Cosines - Certain SAS cases could freeze program
• Note: Older versions will not be able to open assignments saved with this version

Included in version 2.06 released 8/3/2015:

• Fixed: Crash when saving if previously used folder no longer exists

Included in version 2.05 released 7/20/2015:

• New Topic: Sample Spaces and The Fundamental Counting Principle
• New Topic: Independent and Dependent Events
• New Topic: Independent and Dependent Events Word Problems
• New Topic: Mutually Exclusive Events
• New Topic: Mutually Exclusive Events Word Problems
• Fixed: Classifying Conics - Checkboxes for conic types had no effect
• Fixed: Presentation View - Displayed wrong directions in 3-up mode
• Fixed: Presentation View - Lines too long after creating new problems
• Fixed: [Windows] Uncommon error when using the network

Included in version 2.04.40 released 3/31/2015:

• Fixed: Activation data unrecognized under special circumstances
• Fixed: [Windows] Help files broken by previous release
• Fixed: Order of Operations - Radio buttons reversed

Included in version 2.04.20 released 3/23/2015:

• Improved: [Windows] "Export to clipboard as bitmap" uses a transparent background

Included in version 2.04 released 3/17/2015:

• New Topic: Permutations
• New Topic: Combinations
• New Topic: Permutations vs Combinations
• New Topic: Probability with Permutations and Combinations
• New Topic: Converting Degrees and Degrees-Minutes-Seconds
• [factorial(n)]
• [perm(n, r)]
• [comb(n, r)]
• Improved: Better support for proxies
• Improved: Support for HiDPI Mac Retina displays
• Improved: Print options window - Some settings are now persistent
• Improved: Presentation View - Use arrow keys to navigate between questions
• Improved: Question set updates free response/multiple-choice when all questions have changed
• Improved: [Mac] Activation also checks /Library/Preferences/ks-config.txt for serial numbers
• Fixed: [Windows] Crash when printing with certain printers
• Fixed: Crash when loading an assignment with over 80 custom questions
• Fixed: Custom question answer was never choice A
• Fixed: Paper size set before printing
• Fixed: Cramer's Rule - Fixed directions
• Fixed: Systems of Three Equations - Restored the option to "only solve for x"
• Fixed: Center of circle wasn't appearing

Included in version 2.03 released 9/19/2014:

• Fixed: Preference for question layout mode not correctly loaded
• Fixed: Issues with automatic spacing and highlighting questions when using tight layout
• Fixed: In Presentation View, graphing problems display choices more compactly
• Fixed: Printing blank pages on HP LaserJet 1018, 1020, and 1022 among others
• Fixed: Logs and Exponents as Inverses - problem with slider

Included in version 2.02 released 8/5/2014:

• New: Software uses system proxy when necessary
• Improved: Activation window has taskbar entry
• Improved: Remembers the last directory used when saving and opening files
• Fixed: [Windows only] Possible crash when loading an assignment with a lot of custom questions
• Fixed: [Mac only] Application stops responding to hover events
• Fixed: Activation from before v2.0 sometimes not recognized
• Fixed: Export to clipboard sometimes cuts off choices B and D
• Fixed: Help contents could become unusable
• Fixed: Word wrap when modifying a question
• Fixed: Memory leak

Included in version 2.01 released 7/28/2014:

• Fixed: Could crash when opening an assignment from a different program

Included in version 2.00 released 7/23/2014:

• New: Print to PDF
• New: Filter for topic list
• New: Zoom while viewing on screen
• New: "More like these" button in presentation mode
• New: Show where punch holes will go on the page
• New: Print only an answer sheet
• New: When printing, page range is enabled
• New: Page elements are outlined when hovered
• New: Double-click on directions to change them
• New: When merging assignments, options to put similar topics together or put them end-to-end
• New: Highlight and go to the questions in a question set (menu command or shift-click)
• New: Site licenses can be activated per-machine if run by the administrator
• Ctrl-Click on a question
• Shift-Click on a question
• Ctrl-Shift-Click on a question
• Shift-Click in a empty area of a page
• Ctrl-Shift-Click in a empty area of a page
• Shift-Click on a question set
• Ctrl-Shift-Click on a question set
• Improved: Assignment files are drastically smaller
• Improved: Sidebar is dockable on either side, can be floated, and position reset
• Improved: Auto-spacing doesn't leave dead space at bottom of each page
• Improved: Preview when editing directions
• Improved: Keyboard shortcuts work no matter where the focus is
• Improved: Scale number of questions window more user-friendly
• Fixed: Minor bugs in seven topics

Included in version 1.56 released 8/14/2013:

• Fixed: Graphing Exponential Functions - Correct choice used lighter shade of blue
• Fixed: Radical Equations could be missing a solution
• Fixed: Graphs of Polynomial Functions - Inflection points sometimes listed as local extrema
• Fixed: Properties of Exponents - Occasionally answer wasn't fully simplified
• Fixed: Dividing Polynomials - Occasionally polynomial was evenly divisible when it shouldn't have been
• Fixed: Graphing Rational Functions - Minor UI issue
• Fixed: Geometric Sequences - Given information sometimes allowed for two possible common ratios
• Fixed: Dividing Polynomials could freeze
• Fixed: Systems of Equations by Elimination - "No solution" occasionally should have been "Infinite solutions"

Included in version 1.55 released 12/11/2012:

• New: Graphs can be added to custom questions
• Improved: Graphing and Graph Paper utility more powerful and easier to use
• Improved: Support for loading files from Infinite Calculus
• Improved: Faster save/load
• Fixed: Answer for Factoring Quadratic Expressions sometimes incorrect
• Fixed: Choices for Evaluating Functions with a variable operand could contain wrong variable
• Fixed: Choices for Function Operations with a variable operand could contain wrong variable
• Fixed: Function Operations, functions when composed with self could provide the wrong answer
• Fixed: Custom questions with an illegal expression could freeze the program
• Fixed: Certain families of functions graphed incorrectly

Included in version 1.53 released 9/11/2012:

• New: Preference for notation for greatest integer function
• New: Added maximize/restore button to Presentation View
• New: Graphing Absolute Value Equations has options for including coefficients
• Improved: Help files
• Improved: Scroll bars
• Improved: User interface
• Improved: When choices make a question too tall for a page, some choices are removed
• Improved: Algebraic simplification routines are now more efficient
• Improved: Better graphs for: Graphing Absolute Value Equations, Graphing Linear Equations, Graphing Exponential Functions, Graphing Quadratic Functions, Graphing Linear Inequalities, Graphing Systems of Linear Inequalities
• Improved: Better number lines for: Multi-Step Inequalities, Compound Inequalities, Absolute Value Inequalities
• Fixed: Wrapping to full-page and half-page could be too wide
• Fixed: Able to graph certain families of functions
• Fixed: Issue involving loading & regenerating an assignment and answers being hidden
• Fixed: Program could ask about changing directions too much
• Fixed: Graphs for Compound Inequalities could omit interval
• Fixed: Double & Half Angle Identities: Button to show more examples did not work
• Fixed: Writing Linear Equations: Answer can't be line given in question

Included in version 1.52 released 5/29/2012:

• Improved: More professional radical signs
• Improved: Graphs of discontinuous functions have breaks and open / closed holes
• Improved: Even less likely to crash when generating questions
• Fixed: Word wrapping could skip blank lines, not wrap where appropriate
• Fixed: Wrapping to full page in a custom question was too wide
• Fixed: Products of powers of e (like 2 e &sup3;) no longer display with a multiplication dot
• Fixed: Most diagrams appeared incorrectly in print preview
• Fixed: Random error message on save or load
• Fixed: Graphing Rational Functions: Open holes in graph could appear as filled holes

Included in version 1.51.02 released on 4/9/2012:

• Fixed: Minimum Windows version was set incorrectly

Included in version 1.51 released 4/5/2012:

• New: Added greatest integer function / floor function to custom questions    Example: Find [int(2x)] when [x=3/5]
• New: Added piecewise functions to custom questions    Example: [eval(f,x)] = [piecewise [x] if [x < 0], [xx] if [x >= 0]]
• Improved: Faster! Optimized rendering of questions to screen
• Improved: Faster! Optimized graphing routines
• Improved: Improved graphing capabilities
• Improved: Diagrams drawn more smoothly on screen
• Fixed: Rewriting Logarithms - Numeric problems sometimes had bad values
• Fixed: Evaluating Logarithms - Problems sometimes had bad values
• Fixed: Graphs could omit holes
• Fixed: Graphs of constant functions or those involving e and π could be incorrect
• Fixed: Minor indentation issue in custom questions
• Fixed: Horizontal asymptotes could be drawn beyond a graph's area

Included in version 1.50 released 3/15/2012:

• New: Presentation View window is resizeable
• New: Presentation View has option to automatically hide the answers when a new question is displayed
• New: High-level filter to prevent questions from containing an illegal expression
• Improved: Function notation can now be edited
• Improved: Faster! Optimized the simplification of mathematical expressions
• Improved: Faster! Improved undo/redo algorithm
• Improved: Smaller executable size
• Improved: "Current Question Sets" list easier to use
• Improved: Options windows resize more smoothly
• Fixed: Equation of Parabolas could freeze
• Fixed: Geometric Series questions could list "Illegal Expression" as a choice
• Fixed: Graphing Exponential Functions could freeze
• Fixed: Systems of Equations Word Problems could freeze
• Fixed: Punctuation in some word problems
• Fixed: Certain expressions in a custom question would cause the software to crash
• Fixed: Expressions like root × term would not print a multiplication dot
• Note: Beginning with this version, Windows XP SP3 is the minimum required version of Windows

Included in version 1.45 released 4/12/2011:

• New: Assignments from this program can be opened and modified by our other programs          (Assignments saved with v1.45 or greater can be opened by other programs v1.45 or greater)
• New: Student data fields (name, date, period) can be renamed
• New: Additional student data field available
• New: Add & Continue is available when modifying an existing question set
• New: Link to this details page when a software update is available
• New: Product serial numbers can be placed in config.txt to facilitate enterprise installations
• Improved: Better backwards- and future-compatibility
• Fixed: Assignments with quotes in the title don't prevent Save As
• Fixed: Quotients could be sometimes be simplified incorrectly
• Fixed: Choices for dilations sometimes inappropriate
• Fixed: Dilations rounding x- and y-coordinates
• Fixed: Function Operations could have "Illegal Expression" as an answer or as a choice
• Fixed: Multi-Step Equations: Program could freeze
• Fixed: Dividing Radical Expressions: Program could freeze
• Fixed: Add & Continue respects change in problem type
• Fixed: Powers of i are correctly displayed

Included in version 1.42 released on 6/28/2010:

• New: Automatically checks for updates
• New: List topics by index order or suggested order

Included in version 1.40 released 2/8/2010:

• New Preference: 'Spacious' or 'tight' layout of questions on page
• Improved: Question sets with one question are more intelligently spaced
• Improved: Graphs with small ranges now look better
• Improved: Options screen now resizeable
• Fixed: Directions occasionally orphaned at bottom of page
• Fixed: Correct numbers changed because zeros at the end of a number were deleted (50 --> 5)

Included in version 1.08.20 released 5/22/2009:

• Changed: Minor change to license agreement so that renewals extend the termination date instead of beginning a new term.

Included in version 1.08 released 4/10/2009:

• New: Possible to change directions for a set without regenerating questions
• Improved: Changing directions cascades changes to appropriate neighbors
• Correction: Answers to Properties of Exponents could have wrong sign
• Correction: Inequalities were sometimes solved incorrectly
• Fixed: Software sometimes failed to renumber questions in assignment

Included in version 1.07 released 1/6/2009:

• New: Trig. equations that don't require factoring
• Correction: Function operations / linear combinations answers sometimes wrong
• Fixed: Software crashes when starting if closed when side panel is minimized

Included in version 1.06 released 12/4/2008:

• Improved: Isolate up to four questions on screen at once
• Improved: Support for computers with multiple processors
• Improved: User interface: Toolbar + Preferences
• Fixed: Obscure error involving selecting a question and scaling the assignment

Included in version 1.03 released 10/1/2008:

• New: Export individual questions as bitmaps
• Improved: Custom questions wrap to whole/half page
• Improved: Insert special symbols and math in custom questions
• Improved: Insert 'blanks' into math text
• Improved: Line thickness preference also now controls darkness of grid lines in graphs
• Correction: Writing logs in terms of others sometimes created duplicate questions
• Fixed: Internet calls would sometimes report wrong error

Included in version 1.02 released 9/18/2008:

• Correction: Question type was not saving all of its options
• Correction: Equations of Hyperbolas description was sometimes wrong
• Correction: Geometric Series directions was sometimes wrong
• Correction: Binomial Theorem type could cause the program to freeze
• Correction: Quadratic/Linear systems sometimes had the wrong answer
• Correction: Rational Exponents answers now correct
• Fixed: Internet calls could freeze program

Try Infinite Algebra 2 Today!

Discover the power and flexibility of our software firsthand with a free, 14-day trial. Installation is fast and simple. Within minutes, you can have the software installed and create the precise worksheets you need -- even for today's lesson.

Use each trial for up to 14 days. The trial version is identical to the retail version except that you cannot print to electronic formats such as PDF.

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Algebra II : Simplifying Expressions

Study concepts, example questions & explanations for algebra ii, all algebra ii resources, example questions, example question #1 : simplifying expressions.

Simplify x(4 – x) – x(3 – x).

You must multiply out the first set of parenthesis (distribute) and you get 4x – x 2 . Then multiply out the second set and you get –3x + x 2 . Combine like terms and you get x.

x(4 – x) – x(3 – x)

4x – x 2  – x(3 – x)

4x – x 2 – (3x – x 2 )

4x – x 2 – 3x + x 2 = x

Example Question #51 : Trinomials

Factor the numerator and denominator:

Cancel the factors that appear in both the numerator and the denominator:

Example Question #2 : How To Divide Monomial Quotients

Simplify the following:

First, let us factor the numerator:

Find the product:

First, mulitply the mononomial by the first term of the polynomial:

Second, multiply the monomial by the second term of the polynomial:

Add the terms together:

Multiply, expressing the product in simplest form:

Cross-cancel the coefficients by dividing both 15 and 25 by 5, and both 14 and 21 by 7:

Now use the quotient rule on the variables by subtracting exponents:

Example Question #2 : Simplifying Expressions

In this problem, you have two fractions being multiplied. You can first simplify the coefficients in the numerators and denominators. You can divide and cancel the 2 and 14 each by 2, and the 3 and 15 each by 3:

You can multiply the two numerators and two denominators, keeping in mind that when multiplying like variables with exponents, you simplify by adding the exponents together:

Any variables that are both in the numerator and denominator can be simplified by subtracting the numerator's exponent by the denominator's exponent. If you end up with a negative exponent in the numerator, you can move the variable to the denominator to keep the exponent positive:

Example Question #3 : How To Factor A Variable

Factor the expression:

To find the greatest common factor, we need to break each term into its prime factors:

Example Question #1 : Monomials

To expand, multiply 8x by both terms in the expression (3x + 7).

8x multiplied by 3x is 24x².

8x multiplied by 7 is 56x.

Therefore, 8x(3x + 7) = 24x² + 56x.

None of the other answers are correct.

First, distribute –5 through the parentheses by multiplying both terms by –5.

Then, combine the like-termed variables (–5x and –3x).

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Simplifying Algebraic Expressions (Algebra 2)

In Algebra 2, algebraic expressions are one of the most important concepts students encounter. They learn how to simplify them or rewrite them in a simplified way. To achieve this, they apply the properties of real numbers and produce an equivalent form of an expression.

Indeed, all the x’s and y’s can come across as tricky, but they’re certainly not impossible to learn! Math teachers can adopt various strategies to support students in becoming fluent in simplifying algebraic expressions. Read on to find out more.

Algebraic Expressions Definition

For starters, remind students of the definition of an algebraic expression. By now, most students should be able to tell you that an algebraic expression is a mathematical expression comprising constants, variables, and operations (such as addition, subtraction, multiplication, etc.).

Give an example, such as 8x + 4. This is a simple algebraic expression, as it contains two constants (the number 8 and 4 which don’t change), a variable (the letter x, which can change), and an operation (subtraction).

Remind children that when algebra problems come as word problems, we must transform these words into algebraic expressions, known as writing algebraic expressions. Substituting a number for each variable and doing the operation is called evaluating algebraic expressions.

Finally, explain that simplifying an algebraic expression means that we’re turning a long expression into something that we can easily make sense of. Then, you can provide an example. For instance, you can say that by using simplification, we can turn 2x 5y – y2 into 4xy.

You may also want to check out our article on writing and evaluating algebraic expressions.

Teaching How to Simplify Algebraic Expressions

Bell-work activity.

In order for students to be able to simplify an algebraic expression, they need to have a solid grasp of the properties of real numbers. This is why it’s advisable to do a few exercises so that you can review previously acquired knowledge in this regard.

You can use this simple Bell-Work Worksheet for this purpose. Print out a sufficient number of copies and distribute them to each student. The worksheet contains exercises on properties of real numbers, such as the distributive property, the commutative property, associative property, etc.

Simplifying Algebraic Expressions

Start by writing an easier example on the whiteboard, such as:

5x – 8 + 3 (2x – 5) = ?

Explain that by applying the distributive property, we’ll get the following expression:

5x – 8 + 6x – 15

Point out to students that when we simplify an algebraic expression, we also need to combine similar terms. Illustrate the like expressions in the above example. You can use a marker to highlight the like expressions in different colors. That is:

That means that:

5x + 6x = 11x

– 8 – 15 = – 23

11x – 23

You can use this video in your classroom to present the process of simplifying algebraic expressions. It starts with simpler examples and gradually moves on to more complicated expressions.

Finally, distribute this Guided Notes Worksheet for even more challenging expressions.

Activities to Practice Simplifying Algebraic Expressions

In Algebra 2, algebraic expressions and their simplification can be mastered with the help of different engaging activities in your classroom. Use the following activities for group work, or adjust them to individual work if you’re a homeschooling parent.

Online Game

Divide children into pairs and explain that they’ll play an online game to practice how to simplify algebraic expressions. Make sure that each student has a suitable device.

Explain to students that each person in the pair will play the game individually on their device. The game consists of answering different math questions related to simplifying algebraic expressions, such as:

Simplify the following expression:

-3(x + y) + 5(x – y)

The game usually offers multiple answers from which the student needs to select one. For each question that a student answers correctly, they score points. In the end, the students compare their scores and the one with the highest score wins the game.

To implement this activity in your classroom, print out enough copies of this Assignment Worksheet , depending on the number of students in your class. Then, divide students into groups of three or four and hand out the copies.

The worksheet contains math problems connected to simplifying algebraic expressions or writing an algebraic expression to the given verbal expression. Each group works together to solve the math problems in the worksheet.

In the end, each group selects one representative to present their answers in front of the class, as well as explain how they reached a specific solution. This activity will encourage cooperation within a group, as well as reinforce presentation skills.

Before You Leave…

In algebra 2, algebraic expressions and the process of simplifying them can be an engaging experience for children if you’re equipped with the right resources!

So, if you liked our math strategies in this article, make sure to check out our resources on simplifying algebraic expressions:

• 1-2 Assignment (PDF)
• 1-2 Assignment SE (PDF)
• 1-2 Bell Work (PDF)
• 1-2 Bell Work SE (PDF)
• 1-2 Exit Quiz – (PDF)
• 1-2 Exit Quiz SE (PDF)
• 1-2 Guided Notes SE (PDF)
• 1-2 Guided Notes TE (PDF)
• 1-2 Lesson Plan (PDF)
• 1-2 Online Activity (PDF)
• 1-2 Slide Show (PDF)

To get the Editable versions of these files, join us inside the Math Teacher Coach Community:

• 1-2 Assignment ( Doc – Members Only )
• 1-2 Bellwork ( Doc – Members Only )
• 1-2 Exit Quiz ( Doc – Members Only )
• 1-2 Guided Notes SE ( Doc – Members Only )
• 1-2 Guided Notes TE ( Doc – Members Only )
• 1-2 Lesson Plan ( Doc – Members Only )
• 1-2 Online Activity ( Doc – Members Only )
• 1-2 Slide Show (PPT – Members Only )

This article is based on:

Unit 1 – Tools of Algebra

• 1-1 Properties of Real Numbers
• 1-2 Algebraic Expressions
• 1-3 Solving Equations
• 1-4 Solving Inequalities
• 1-5 Absolute Value Equations and Inequalities
• 1-6 Probability

Do You Need More Math Resources?

If you’re looking for more math materials for children of all ages, become a member of our Math Teacher Coach community or sign up for our emails to receive loads of free content! Feel free to also check out our blog ! You’ll find plenty of resources for all grades that will make teaching math a breeze!

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The Algebra Calculator is a versatile online tool designed to simplify algebraic problem-solving for users of all levels. Here's how to make the most of it:

• Begin by typing your algebraic expression into the above input field, or scanning the problem with your camera.
• After entering the equation, click the 'Go' button to generate instant solutions.
• The calculator provides detailed step-by-step solutions, aiding in understanding the underlying concepts.
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• How do you solve algebraic expressions?
• To solve an algebraic expression, simplify the expression by combining like terms, isolate the variable on one side of the equation by using inverse operations. Then, solve the equation by finding the value of the variable that makes the equation true.
• What are the basics of algebra?
• The basics of algebra are the commutative, associative, and distributive laws.
• What are the 3 rules of algebra?
• The basic rules of algebra are the commutative, associative, and distributive laws.
• What is the golden rule of algebra?
• The golden rule of algebra states Do unto one side of the equation what you do to others. Meaning, whatever operation is being used on one side of equation, the same will be used on the other side too.
• What are the 5 basic laws of algebra?
• The basic laws of algebra are the Commutative Law For Addition, Commutative Law For Multiplication, Associative Law For Addition, Associative Law For Multiplication, and the Distributive Law.

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How to simplify your expression, typing exponents, simplifying expressions video lesson.

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Solve equations and simplify expressions

• Solving equations I
• Solving equations II
• Solving equations III

In algebra 1 we are taught that the two rules for solving equations are the addition rule and the multiplication/division rule. The addition rule for equations tells us that the same quantity can be added to both sides of an equation without changing the solution set of the equation.

$$\begin{array}{lcl} 4x-12 & = & 0\\ 4x-12+12 & = & 0+12\\ 4x & = & 12\\ \end{array}$$

Adding 12 to each side of the equation on the first line of the example is the first step in solving the equation. We did not change the solution by adding 12 to each side since both the second and third equations have the same solution. Equations that have the same solution sets are called equivalent equations.

The multiplication/division rule for equations tell us that every term on both sides of an equation can be multiplied or divided by the same term (except zero) without changing the solution set of the equation.

$$\begin{array}{lcl} 4x-12 & = & 0\\ 4x-12+12 & = & 0+12\\ 4x & = & 12\\ \frac{4x}{4} & = & \frac{12}{4}\\ x & = & 3\\ \end{array}$$

When we simplify an expression we operate in the following order:

• Simplify the expressions inside parentheses, brackets, braces and fractions bars.
• Evaluate all powers.
• Do all multiplications and division from left to right.
• Do all addition and subtractions from left to right.

A useful rule is the denominator-numerator rule which states that the denominator and numerator may be multiplied by the same quantity without changing the value of the fraction.

$$\frac{(2^{2}-2)}{\sqrt{2}}$$

First we simplify the expression inside the parentheses by evaluating the powers and then do the subtraction within it.

$$\frac{(4-2)}{\sqrt{2}}$$

$$\frac{(2)}{\sqrt{2}}$$

We then remove the parentheses and multiply both the denominator and the numerator by √2.

$$\frac{2\cdot \sqrt{2}}{\sqrt{2}\cdot \sqrt{2}}$$

As a last step we do all multiplications and division from left to right.

$$\frac{2\cdot \sqrt{2}}{2}$$

$$\sqrt{2}$$

Video lesson

Solve the given equation

$$12a\left(\frac{3b-b}{4a}\right)=36$$

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Algebra 2 Worksheets with answer keys

Enjoy these free printable math worksheets . Each one has model problems worked out step by step, practice problems, as well as challenge questions at the sheets end. Plus each one comes with an answer key.

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Simplifying Algebraic Expressions with Two Variables and Six Terms (Addition and Subtraction) (A)

Welcome to The Simplifying Algebraic Expressions with Two Variables and Six Terms (Addition and Subtraction) (A) Math Worksheet from the Algebra Worksheets Page at Math-Drills.com. This math worksheet was created or last revised on 2013-02-14 and has been viewed 167 times this week and 414 times this month. It may be printed, downloaded or saved and used in your classroom, home school, or other educational environment to help someone learn math.

Teacher s can use math worksheets as test s, practice assignment s or teaching tool s (for example in group work , for scaffolding or in a learning center ). Parent s can work with their children to give them extra practice , to help them learn a new math skill or to keep their skills fresh over school breaks . Student s can use math worksheets to master a math skill through practice, in a study group or for peer tutoring .

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Unit 6: Rational exponents and radicals

About this unit.

We previously learned about integer powers—first positive and then also negative. But what does it mean to raise a number to the 2.5 power? In Algebra 2, we extend previous concepts to include rational powers. We'll define how they work, and use them to rewrite exponential expressions in various ways.

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What can QuickMath do?

QuickMath will automatically answer the most common problems in algebra, equations and calculus faced by high-school and college students.

• The algebra section allows you to expand, factor or simplify virtually any expression you choose. It also has commands for splitting fractions into partial fractions, combining several fractions into one and cancelling common factors within a fraction.
• The equations section lets you solve an equation or system of equations. You can usually find the exact answer or, if necessary, a numerical answer to almost any accuracy you require.
• The inequalities section lets you solve an inequality or a system of inequalities for a single variable. You can also plot inequalities in two variables.
• The calculus section will carry out differentiation as well as definite and indefinite integration.
• The matrices section contains commands for the arithmetic manipulation of matrices.
• The graphs section contains commands for plotting equations and inequalities.
• The numbers section has a percentages command for explaining the most common types of percentage problems and a section for dealing with scientific notation.

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