1. The Distributive Property

2. The Distributive Property: Multiply by a Monomial
The product of a and (b+c) is given by:
a( b + c ) = ab + ac
Example: Simplify 2x(x – 9)
Every term inside the parentheses is multiplied by a. x -9
Area Method:
“Arrow” Method: 2x
2x2
-18x
Do NOT forget to answer the question.

3. These represent the same area. They must be equal.
The Generic Rectangle
(x + 4)
(x + 2)
Distribute:
Area as a Product:
These represent the same area. They must be equal.
+ 2 2x 8
Area as a Sum: x2 4x x
Therefore: x
+ 4

4. The Distributive Property: Multiply with the Area Model
3 terms times 2 terms
Distribute: ( x2 - x + 3 )( x + 5)
x x
A 3x2 box. The box is generic so don’t worry about size. x +5 x3
-x2
+3x
+5x2
-5x
+15
x3 – x2 + 3x + 5x2 – 5x + 15
= x3 + 4x2 – 2x + 15
Notice: Each of the three terms in the first set of parentheses is multiplied by each in the second set of parentheses.

5. The Distributive Property: Arrow Method
Distribute: ( x2 - x + 3 )( x + 5)
Instead of the making a box, you can multiply each of the three terms in the first set of parentheses by each in the second set of parentheses. x3
+ 5x2
– x2
– 5x
+ 3x
+ 15
= x3 + 4x2 – 2x + 15

6. The Distributive Property: FOIL
Write the following as a sum:
( 3x – 2 )( 2x + 7)
Firsts
Outers
Inners
Lasts
Simplify
Multiply the…
6x2
+ 21x
+ -4x
+ -14
= 6x2 + 17x – 14
Mr. Wells considers FOIL to be an F-word. It can only be used in specific instances. It only works for a binomial multiplied by a binomial. It is not worth memorizing.

7. The Distributive Property and Solving Equations
Solve: x +3 +1 x 5 -x
-x2
-3x x x2 5x x +5