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**The Distributive Property**

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**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.

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**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

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**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.

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**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

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**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.

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**The Distributive Property and Solving Equations**

Solve: x +3 +1 x 5 -x -x2 -3x x x2 5x x +5

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