Combining like Terms

Combining like Terms

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

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.

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: \(-4x \ + \ 4 \ + 2x= -2x + 4 \)

Example 2:

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

Solution:

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

Example 3:

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

Solution:

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

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

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

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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