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How to Collect Like Terms in Algebra (Mathematics Lesson)

Collecting Like Terms in Algebra

Like terms can be collected together to simply 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.

An Example Question

Simplify the expression below by collecting like terms.

x plus 3 y plus 5 x plus 2 minus y plus x
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.

Step 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.

Step 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

Step 4

Put the expression together.

The expression has become:

7 x plys 2 y plus 2

Another Real Example of How to Collect Like Terms in Algebra

The slider below shows a real example of how to collect like terms.

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Here's a third test on collecting like terms.

Note

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.