# The Distributive Property

To solve expressions in the form of a(b + c), we need to use the distributive property or the distributive property of multiplication.

## Step by step guide to use the distributive property correctly

• Distributive Property:
$$\color{blue}{a \ (b \ + \ c)=ab \ + \ ac}$$

### Example 1:

Simplify. $$(- \ 2)(x \ – \ 3)=$$

Solution:

Use Distributive Property formula: $$a \ (b \ + \ c)=ab \ + \ ac$$
$$(-2)(x-3)=-2x+6$$

### Example 2:

Simplify. $$(5)(6 \ x \ – \ 3)=$$

Solution:

Use Distributive Property formula: $$a \ (b \ + \ c)=ab \ + \ ac$$
$$(5)(6 \ x \ – \ 3)=30 \ x \ – \ 15$$

### Example 3:

Simplify. $$(5x-3)(–5)=$$

Solution:

Use Distributive Property formula: $$a(b+c)=ab+ac$$
$$(5x-3)(–5)=-25x+15$$

### Example 4:

Simplify $$(-8)(2x-8)=$$

Solution:

Use Distributive Property formula: $$a(b+c)=ab+ac$$
$$(-8)(2x-8)=-16x+64$$

## Exercises

### Use the distributive property to simplify each expression.

• $$\color{blue}{– (– 2 – 5x)}$$
• $$\color{blue}{(– 6x + 2)(–1)}$$
• $$\color{blue}{(– 5) (x – 2)}$$
• $$\color{blue}{(– 2x) (– 1 + 9x) – 4x (4 + 5x)}$$
• $$\color{blue}{3 (– 5x – 3) + 4(6 – 3x)}$$
• $$\color{blue}{(– 2)(x + 4) – (2 + 3x)}$$

• $$\color{blue}{5x + 2}$$
• $$\color{blue}{6x – 2}$$
• $$\color{blue}{–5x + 10}$$
• $$\color{blue}{– 38x^2 – 14x}$$
• $$\color{blue}{– 27x + 15}$$
• $$\color{blue}{– 5x – 10}$$