Welcome to our 6th Grade Distributive Property Worksheets.

Here you will find a range of algebra worksheets to help you learn how to use the distributive property to expand and factorize a range of expressions.

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This page is all about using the distributive property to expand and factorize a range of expressions.

We have split the worksheets up into 4 different sections:

- Evaluate the expression - work out the value of different algabraic expressions;
- Expand the expression - use the distributive property to multiply out the brackets;
- Factorize the expression - use the distributive property to factorize different expressions.
- Mixed questions involving all 3 of the above.

By splitting the algebra up into sections, you only need to concentrate on one aspect at a time!

Each question sheet comes with its own separate answer sheet.

Want to test yourself to see how well you have understood this skill?.

- Try our NEW quick quiz at the bottom of this page.

What is an algebraic expression?

An expression is a mathematical statement where variables and operations are combined.

Examples

- 2a + 5 is an expression involving the variable a
- 5(y
^{2}- 6) is another expression

How to Evaluate an Expression

When we are evaluating the value of an expression, we work out the value of the expression when we give a value to the variable.

Examples

- 2(p + 5) has a value of 22 when p = 6 because 2(6 + 5) = 2 x 11 = 22
- 3(12 - q) has a value of 21 when q = 5 because 3(12 - 5) = 3 x 7 = 21
- 8(n - 2) has a value of 64 when n = 10 because 8 (10 - 2) = 8 x 8 = 64
- 8(n - 2) has a value of 0 when n = 2 because 8 (0 ) = 8 x 0 = 0

How to Expand an Expression

When we are expanding an expression, we multiply out the factors.

Examples

- 2(p + 5) = 2 x p + 2 x 5 = 2p + 10
- 3(12 - q) = 3 x 12 - 3 x q = 36 - 3q
- 8(n - 2) = 8 x n - 8 x 2 = 8n - 16
- 5(y + 3z) = 5 x y + 5 x 3z = 5y + 15z

How to Factorize an Expression

When we are factorizing an expression, we try to find the greatest common factor of all the numbers and take it out as a factor.

Examples

- 3n + 15 = 3(n + 5) - greatest common factor of 3 and 15 is 3.
- 4p + 32 = 4(p + 8) - the greatest common factor of 4 and 32 is 8.
- 20 - 8y = 4(5 - 2y) - the greatest common factor of 20 and 8 is 4.
- 4a - 10b + 6c = 2(2a - 5b + 3c) - the greatest common factor of 4, 10 and 6 is 2.
- 35d + 42 = 7(5d + 6) - the greatest common factor of 35 and 42 is 7.

These sheets involve working out the value of the expression using PEMDAS and order of operations.

The first sheets is a multiple choice sheet with only numbers in the expressions.

The second sheet involves finding the value of the expression with only numbers in the expression.

The third sheet involves finding the value of the expression with numbers and variables in the expression.

When we are expanding an expression, we multiply out the factors.

Sheet 1 is a multiple choice sheet where you match the factorized expression with the correct expanded expression.

Sheet 2 involes writing the factorized expression as an expanded expression.

When we are factorizing an expression, we try to find the greatest common factor of all the numbers and take it out as a factor.

Sheet 1 is a multiple choice sheet where you match the expression with the correct factorized expression.

Sheet 2 involes writing the expression as a factorized expression.

These questions involve expanding, factorizing and evaluating different expressions..

They are a combination of questions from all the above categories.

Take a look at some more of our worksheets similar to these.

If you are looking for some basic algebra worksheets to use with your child to help them understand simple equations then try our selection of basic algebra worksheets.

There are a range of 6th grade math worksheets covering the following concepts:

- Generate the algebra - and write your own algebraic expressions;
- Calculate the algebra - work out the value of different expressions;
- Solve the algebra - find the value of the term in the equation.

The Mathway Calculator is a great way to solve algebra problems that you can type into a calculator.

Try using this online calculator tool to solve one of your problems and watch it work!

There are a range of calculators to choose from to meet your needs.

The Mathway problem solver will answer your problem instantly and also give you a link to view each of the steps needed.

If you choose to 'View the steps' you will be directed to the Mathway website where you will be able to see in more detail each of the steps needed to solve the problem. Please note that Mathway may charge you a small fee for this!

Are you stuck on a quadratic equation and don't know what to do?

Are you looking for some worksheets on factorising quadratic equations to print out?

Take a look at our support pages on quadratic equations where you will hopefully find what you are looking for.

If you are looking for a fun printable algebra game to play then try out our algebra game page.

You will find a range of algebra games that make learning algebra fun and non-threatening.

The only equipment you need is a scientific calculator, some dice, and a few counters!

The sheets in this section involve using parentheses and exponents in simple calculations.

There are also lots of worksheets designed to practice and learn about PEMDAS.

Using these worksheets will help your child to:

- know and understand how parentheses works;
- understand how exponents work in simple calculations.
- understand and use PEMDAS to solve a range of problems.

This interactive equality explorer has been produced by PhET Interactive Simulations at the University of Colorado.

It is a useful tool for exploring different ideas including negative numbers and algebra equations and equality.

Probably the most useful part of the app is to use the 'Solve It' section once you are confident how it works.

You can then select your level of difficulty and start solving some algebraic equations by getting your variables onto one side of the equation and the numerical values on the other, and then multiplying or dividing the equation until you find the value of the required variable.

Our quizzes have been created using Google Forms.

At the end of the quiz, you will get the chance to see your results by clicking 'See Score'.

This will take you to a new webpage where your results will be shown. You can print a copy of your results from this page, either as a pdf or as a paper copy.

For incorrect responses, we have added some helpful learning points to explain which answer was correct and why.

We do not collect any personal data from our quizzes, except in the 'First Name' and 'Group/Class' fields which are both optional and only used for teachers to identify students within their educational setting.

We also collect the results from the quizzes which we use to help us to develop our resources and give us insight into future resources to create.

For more information on the information we collect, please take a look at our Privacy Policy

We would be grateful for any feedback on our quizzes, please let us know using our Contact Us link, or use the Facebook Comments form at the bottom of the page.

This quick expressions and equations 6th grade quiz tests your knowledge and skill at generating and calculating expressions, as well as solving equations.

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