1. Distributive Property
To simplify some expressions we may need to use the Distributive Property
Do you remember it?
Distributive Property
a ( b + c ) = ba + ca

2. Distributive – multiply across the parentheses.
Using the distributive property lets you multiply each element inside the parentheses by the element outside the parentheses. Consider the problem to the left. The number in front of the parentheses is “looking” to distribute (multiply) its value with all of the terms inside the parentheses.

3. Examples
Example 1: 6(x + 2) Distribute the 6. 6 (x + 2) = x(6) + 2(6) = 6x + 12
Example 2: -4(x – 3)
Distribute the –4.
-4 (x – 3) = x(-4) –3(-4)
= -4x

4. Practice Problem Try the Distributive Property on -7 ( x – 2 ) .
Be sure to multiply each term by a –7.
-7 ( x – 2 ) = x(-7) – 2(-7)
= -7x
Notice when a negative is distributed all the signs of the terms in the ( )’s change.

5. Examples with 1 and –1. Example 3: (x – 2) = 1( x – 2 ) = x(1) – 2(1)
Notice multiplying by a 1 does nothing to the expression in the ( )’s.
Example 4: -(4x – 3)
= -1(4x – 3)
= 4x(-1) – 3(-1)
= -4x + 3
Notice that multiplying by a –1 changes the signs of each term in the ( )’s.