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

## Related Topics

- How to Translate Phrases into an Algebraic Statement
- How to Simplify Variable Expressions
- How to Simplify Polynomial Expressions
- How to Use the Distributive Property
- How to Evaluate One Variable

## 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

## Answers

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