# How to Combine Like Terms? (+FREE Worksheet!)

Learn how to combine 'like' terms (terms with the 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.

### Combining like Terms – Example 1:

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

Solution:

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

Now, combine like terms: $$-4x + 2x= -2x$$

Then: $$-4x \ + \ 4 \ + 2x= -2x + 4$$

### 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: $$8x\ – 2x = 6x$$

Then: $$8x-6\ – 2x = 6x\ – 6$$

### Combining like Terms – Example 4:

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

Solution:

First use Distributive Property formula: $$a(b+c)=ab+ac$$
$$(-3)(2x-2)=-6x+6$$
Now, combining like terms: $$6+6=12$$
Then: $$-6x+6+6=-6x+12$$

## Exercises for Combining like Terms

### Simplify each expression.

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

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

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