How to Combine Like Terms

How to Combine Like Terms

Learn how to combine ‘like’ terms (terms with same variable and same power) to simplify algebraic expressions.

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Step by step guide to combining like terms

  • Terms are separated by “\(+\)” and “\(–\) “signs.
  • Like terms are terms with the same variables and same powers.
  • Be sure to use the “\(+\)” or “\(–\) “that is in front of the coefficient.

Combining like Terms – Example 1:

Simplify this expression. \((-2)(2x \ -2)+2x=\)

Solution:

First use Distributive Property formula: \(a(b \ + \ c)=ab \ + \ ac\)
\((- 2)(2 \ x \ -2)=-4x \ + \ 4 \)

Then, combine like terms: \(-4x \ + \ 4 \ + 2x= -2x + 4 \)

Combining like Terms – Example 2:

Simplify this expression. \(4(- \ 2 x \ + \ 6)=\)

Solution:

Use Distributive Property formula: \(a(b \ + \ c)=ab \ + \ ac\)
\(4 \ − \ 2x \ + \ 6= \ − \ 8 x \ + \ 24 \)

Combining like Terms – Example 3:

Simplify this expression. \(8x \ – 6 \ – 2x = \)

Solution:

Combine like terms: \(8x-6 – 2x = 6x – 6 \)

Combining like Terms – Example 4:

Simplify this expression. \( (-3)(2x-2)+6=\)

Solution:

First use Distributive Property formula: \(a(b+c)=ab+ac \)
\( (-3)(2x-2)+6=-6x+6+6 \)
Combining like Terms:
\(-6x+6+6=-6x+12 \)

Exercises for Combining like Terms

Simplify each expression.

  • \(\color{blue}{(– 11x) – 10x}\)
  • \(\color{blue}{3x – 12 – 5x}\)
  • \(\color{blue}{13 + 4x – 5}\)
  • \(\color{blue}{(– 22x) + 8x}\)
  • \(\color{blue}{2 (4 + 3x) – 7x}\)
  • \(\color{blue}{(– 4x) – (6 – 14x)}\)

Download Combining like Terms Worksheet

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Answers

  • \(\color{blue}{–21x}\)
  • \(\color{blue}{–2x – 12}\)
  • \(\color{blue}{4x + 8}\)
  • \(\color{blue}{–14x}\)
  • \(\color{blue}{– x + 8}\)
  • \(\color{blue}{10x – 6}\)

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