Collecting Like Terms in Algebra
(KS3, Year 7)

The Lesson

Like terms can be collected together to simplify an expression in algebra. Collecting like terms can make a long, complicated expression into a short, simple one.

x plus 3 y plus 5 x plus 2 minus y plus x equals 7 x plus 2 y plus 2

How to Collect Like Terms in Algebra

Collecting like terms is easy.

Question

Simplify the expression below by collecting like terms.
x plus 3 y plus 5 x plus 2 minus y plus x

Step-by-Step:

1

Identify the like terms.
  • Identify the x terms: x, 5x and x.

    collect the x terms
  • Identify the y terms: 3y and -y.

    collect the y terms
  • Identify the number terms: 2.

    collect the number terms

Read more about identifying the like terms.

2

Collect the like terms together. Bring the x terms next to each other. Bring the y terms next to each other. Bring the number terms next to each other.

collect like terms together Don't forget: When you collect like terms, bring the sign in front of the term with it.

3

Add and/or subtract the like terms together.
  • Add the x terms together:

    x plus 5 x plus x
  • Subtract the y terms from each other:

    3 y minus y
  • Add the number terms together. In our example, there is only one number term.

    2
Read more about how to add like terms in algebra Read more about how to subtract like terms in algebra

4

Put the expression together. The expression has become:

7 x plys 2 y plus 2

Answer:

We have collected the like terms to simplify the expression:
x + 3y + 5x + 2 − y + 2 = 7x + 2y + 2

Lesson Slides

The slider below shows a real example of how to collect like terms. Open the slider in a new tab

What Is a Like Term in Algebra?

Like terms are terms with the same combination of letters (and/or brackets). The only difference is the sign or number in front of the group of letters. Each letter (and/or bracket) in a like term must have the same exponents - the number that sits to the top-right of the letter.

What Is a Term in Algebra?

A term is a collection of numbers, letters and brackets all multiplied together. Terms are separated by + or − signs in an algebraic expression.
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See Also

What is algebra? What is a term? What is an expression? What is a like term? Adding like terms Subtracting like terms