2 The Distributive Property: Multiply by a Monomial The product of a and (b+c) is given by:a( b + c ) = ab + acExample: Simplify 2x(x – 9)Every term inside the parentheses is multiplied by a.x-9Area Method:“Arrow” Method:2x2x2-18xDo 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.+ 22x8Area as a Sum:x24xxTherefore:x+ 4
4 The Distributive Property: Multiply with the Area Model 3 terms times 2 termsDistribute: ( x2 - x + 3 )( x + 5)x xA 3x2 box. The box is generic so don’t worry about size.x+5x3-x2+3x+5x2-5x+15x3 – x2 + 3x + 5x2 – 5x + 15= x3 + 4x2 – 2x + 15Notice: 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)FirstsOutersInnersLastsSimplifyMultiply the…6x2+ 21x+ -4x+ -14= 6x2 + 17x – 14Mr. 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+1x5-x-x2-3xxx25xx+5