1. 6.8 Multiplying Polynomials
CORD Math
Mrs. Spitz
Fall 2006

2. Objectives: After studying this lesson, you should be able to:
Use the FOIL method to multiply to binomials, and
Multiply any two polynomials using the distributive property.

3. Assignment
Worksheet 6.8
Reminder there is a test over chapter 9 after 6.9 and a review for the chapter.

4. Connection:
You know that the area of a rectangle is the product of its length and width. You can multiply 2x + 3 and 5x + 8 to find the area of a large rectangle.
5x cm
8 cm
2x cm
3 cm

5. Connection: (2x + 3)(5x + 8) = 2x(5x + 8) + 3(5x + 8)
But you also know that the area of the large rectangle equals the sum of the areas of the four smaller rectangles, don’t you?

6. Connection: = 10x2 + 16x + 15x + 24 = 10x2 + 31x + 24
(2x + 3)(5x + 8) = 2x · 5x + 2x ·8 + 3 · 5x + 3 ·8
= 10x2 + 16x + 15x + 24
= 10x2 + 31x + 24
This example illustrates a shortcut of the distributive property called the FOIL METHOD.

7. (2x + -3)(4x + 5) = 8x2 + 10x + -12x + -15 = 8x2 + -2x + -15
F.O.I.L.
There is an acronym to help us remember how to multiply two binomials without stacking them.
(2x + -3)(4x + 5)
F : Multiply the First term in each binomial. 2x • 4x = 8x2
O : Multiply the Outer terms in the binomials. 2x • 5 = 10x
I : Multiply the Inner terms in the binomials. -3 • 4x = -12x
L : Multiply the Last term in each binomial. -3 • 5 = -15
(2x + -3)(4x + 5) = 8x2 + 10x + -12x = 8x2 + -2x + -15

8. Use the FOIL method to multiply these binomials:
1) (3a + 4)(2a + 1)
2) (x + 4)(x - 5)
3) (x + 5)(x - 5)
4) (c - 3)(2c - 5)
5) (2w + 3)(2w - 3)

9. Use the FOIL method to multiply these binomials:
6a2 + 3a + 8a + 4 = 6a2 + 11a + 4
x2 + -5x + 4x = x2 - x -20
x2 + -5x + 5x = x2 – 25
2c2 + -5x + - 6x + 15 = 2c2 -11x +15
4w2 + -6w + 6w + -9 = 4w2 - 9
(3a + 4)(2a + 1) =
(x + 4)(x - 5) =
(x + 5)(x - 5) =
(c - 3)(2c - 5) =
(2w + 3)(2w - 3) =

10. Ex. 1 Find (y + 5)(y + 7) Ex. 2 Find (3x - 5)(5x + 2)
(y + 5)(y + 7) = y · y + y · · y + 5 · 7
= y2 + 7y + 5y + 36
= y2 + 12y + 36
Ex. 2 Find (3x - 5)(5x + 2)
(3x - 5)(5x + 2) = 3x · 5x + 3x · · 5x + -5 · 2
= 15x2 + 6x – 25x - 10
= 15x2 - 19y - 10

11. Ex. 3 Find (2x - 5)(3x2 -5x + 4) Ex. 4 Find (x2 – 5x + 4)(2x2 + x – 7)
(2x - 5)(3x2 -5x + 4) = 2x(3x2 -5x + 4) – 5(3x2 -5x + 4)
= 6x3 - 10x2 + 8x - 15x2 +25x -20
= 6x3 – ( )x2 + (8+25)x -20
= 6x3 – 25x2 + 33x -20
Ex. 4 Find (x2 – 5x + 4)(2x2 + x – 7)
(x2 – 5x + 4)(2x2 + x – 7) = x2(2x2 + x - 7) -5x(2x2 + x – 7) +4(2x2 + x – 7)
= 2x4 + x3 – 7x2 – 10x3 - 5x2 + 35x + 8x2 + 4x – 28
= 2x4 + (1 – 10)x3 + (– 7 – 5 + 8)x2 + (35 + 4)x – 28
= 2x4 – 9x3 – 4x2 + 39x – 28

12. x3 + 0x2 + 5x - 6 (x) 2x - 9 -9x3 - 0x2 - 45x + 54 2x4 0x3 10x2 - 12x
Polynomials can also be multiplied in column form. Be careful to align like terms. x3
+ 0x2
+ 5x
- 6
(x) 2x
- 9
-9x3
- 0x2
- 45x
+ 54
2x4
0x3
10x2
- 12x
- 9x3
- 57x