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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) 2x2x x-9 2x22x2 -18x Every term inside the parentheses is multiplied by a. Area Method: “Arrow” Method: Do NOT forget to answer the question.

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The Generic Rectangle Distribute: Area as a Product: Area as a Sum: (x + 4)(x + 2) These represent the same area. They must be equal. Therefore: x2x2 4x4x 2x2x8 x + 4 x + 2

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The Distributive Property: Multiply with the Area Model Distribute: ( x 2 - x + 3 )( x + 5) x 2 -x +3 x +5 x 3 x 3 – x 2 + 3x + 5x 2 – 5x + 15= x 3 + 4x 2 – 2x x2-x2 +5x 2 -5x +3x terms times 2 terms A 3x2 box. The box is generic so don’t worry about size. 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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+ 15 The Distributive Property: Arrow Method Distribute: ( x 2 - x + 3 )( x + 5) x 3 = x 3 + 4x 2 – 2x x 2 – 5x + 3x– x 2 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.

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The Distributive Property: FOIL Write the following as a sum: ( 3x – 2 )( 2x + 7) Firsts Outers Inners Lasts Simplify + -4x = 6x x – x x2 6x2 Multiply the… 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-x x+3 -x2-x2 -3x x x+5 x2x2 5x5x x 5 +1

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