# 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.

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

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