How to Collect Like Terms

Collecting like terms means putting together the parts of an expression that belong together.

This page contains lots of information and support to help you master the math behind collecting like terms.

Scroll down to find out:

• what is a term
• what is a like term
• examples showing what are like terms and what are NOT like terms
• step-by-step guide to collecting like terms
• common mistakes when collecting like terms
• how to collect like terms worksheets

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

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

A term can be a number, a variable or a combination of a combination of a number and variable multiplied together.

Terms are usually separated by + and - signs, but they can be separated in other ways.

In the example above: 3x - 2 = 5y, there are 3 terms:

• 3x
• 2
• 5y

A variable is a symbol, usually a letter, which is used to represent an unknown number or changeable number.

If a variable has a number in front of it, then the number represents the number of 'lots' of the variable and is called the coefficient.

Example: a + 3b

• a and b are both variables
• 3b = 3 'lots' of b = b + b + b
• 3 is called the coefficient of b

Example: 4c + 7d

• c and d are both variables
• 4c = 4 'lots' of c = c + c + c + c
• 7d = 7 'lots' of d = d + d + d + d + d + d + d
• In 4c, the coefficient is 4.
• In 7d, the coefficient is 7.

When we have an algebraic expression, we can sometimes collect like terms and simplify the expression.

However, we can only collect like terms if:

• they both have the same variable [e.g. y and 2y]
• they both have the same power (or exponent), [e.g. 3n² and 5n²]
• then can have different coefficients, [e.g. 2x and 9x]

You can think of like terms as being similar to players on the same team wearing the same kit.

Here are some step by step instructions for collecting like terms.

Step 0) Before you start collecting like terms, multiply out any brackets using the distributive property.

If your expression contains any brackets to multiply [e.g. 3(x + 7) - 2x + 4 ] then do this part first.

Step 1) Identify all the like terms.

A useful tip is to highlight all the like terms. Color-code each variable.

Step 2) Combine the coefficients

Add or subtract the numbers in front of the coefficients of all the like terms.

Step 3) Don't change any of the variable letters

When you are collecting like terms, the variables do not change - the only thing that changes is the coefficient.

Below are some examples showing the steps needed to collect like terms to simplify an expression.

This simple worksheet involves converting between multiplication and repeated addition using like terms.

There is only one variable and no unlike terms.

We have two sheets: 1A and 1B. You can choose which of these sheets you want to use but don't use both!

Sheet 1A has an extra step where you write the expression as a multiplication first.

Sheet 1B misses this step out.

Here are a couple of examples for Sheet 1A

• b + b + b + b = b x 4 = 4b
• y + y + y = y x 3 = 3y
• 6n = n x 6 = n + n + n + n + n + n
• 4g = g x 4 = g + g + g + g

Here are the same examples for Sheet 1B

• b + b + b + b = 4b
• y + y + y = 3y
• 6n = n + n + n + n + n + n
• 4g = g + g + g + g

These sheets all involve collecting and combining like terms.

If you find them tricky, go back and have a look at the examples shown in the worked example section.

The sheets on this page have been designed to factorize and expand a range of simple expressions using the distributive property..

We have a selection of basic algebra worksheets which are aimed at 6th and 7th graders and involve similar skills to the sheets here.

Have a go at these input and output tables.

Test your skills at finding inputs, outputs and rules.

Our easier sheets have rules instead of algebraic functions.

Our harder sheets use algebraic functions.

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!

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 quick combining like terms quiz tests your knowledge and skill at how to collect like terms at a 6th grade level.

The link below will open the quiz in a dedicated quiz page or you can preview a copy of the quiz underneath.

The Math Salamanders hope you enjoy using these free printable Math worksheets and all our other Math games and resources.

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