1. 7.2 Multiplying Polynomials by Monomials
Math 9

2. 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

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

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

5. 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?
6x x

6. 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 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

7. 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 x 8
a (b + c ) = ab + ac

8. 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.

9. `
Jigsaw 4, 5abc, 6ab (on the board), 8abc,12abcdef Practice 7,10,14,15,16