7.2 Multiplying Polynomials by Monomials

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Presentation transcript:

7.2 Multiplying Polynomials by Monomials Math 9

Example 1: Determine the product using an area model: (4 x ) (3x + 5) One way to do this would be to draw a rectangle with side dimensions of 4x and 3x + 5

Calculate the area of each rectangle: A1 = (3x)(4x) = 12x2 A2 = (4x)(5) = 20x The total area is 12x2 +20x

Calculate the product: (2a + 7 ) (8a ) (2a + 7 ) (8a ) (2a)(8a) = 16a2 (7)(8a) = 56a = 16a2 + 56a

Example 2: Calculate the product using algebra tiles: (3x ) (2 x - 5 ) What are the dimensions of the rectangle? (3x ) by (2 x -5) What tiles would you use to completely fill in the rectangle? 6x2 - 15x

A= (7 x ) (5x - 9) Find the product: (2 y ) (5 y - 7 ) (2y)(5y) + (2y)(-7) = 10y2 -14y Example 3. The dimensions of a rectangle are 7 x and 5x - 9 . Determine a polynomial expression for the area of the rectangle. Since the area of a rectangle, A, can be found by multiplying the length by the width, we have A= (7 x ) (5x - 9) A w l

The Distributive Principle To determine this product algebraically, you can use the distributive property A = (7 x ) (5x - 9) = (7x)(5x) + (7x)(-9) =35x2 - 63x The Distributive Principle 4 (5 + 8) = 4 x 5 + 4 x 8 a (b + c ) = ab + ac

Example 4. The dimensions of a rectangular box are x cm by 3x cm by 2x + 4 cm. What is an expression for the surface of the box? 2 A1 +2 A2 + 2 A3 A1 = (3x)(x) = 3x2 A2 = (x)(2x+4) = 2x2 + 4x A3 = (3x)(2x+4) = 6x2 +12x 3x x A1 But remember we have 6 sides on this box which means 2 sides of each 2x + 4 A2 A3 ∗2 = 6x2 = 4x2 + 8x = 12x2 +24x 22x2 + 32x The surface area of the box can be expressed 22x2 + 32x cm2.

` Jigsaw 4, 5abc, 6ab (on the board), 8abc,12abcdef Practice 7,10,14,15,16