6.8 Multiplying Polynomials

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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
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Connection

• (2x 3)(5x 8) 2x(5x 8) 3(5x 8)
• (2x)(5x) 2x(8) (3)(5x) (3)(8)
• 10x2 16x 15x 24
• 10x2 31x 24
• But you also know that the area of the large
  rectangle equals the sum of the areas of the four
  smaller rectangles, dont you?

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Connection

• (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.

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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
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F.O.I.L.
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)
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F.O.I.L.
Use the FOIL method to multiply these binomials

1. 6a2 3a 8a 4 6a2 11a 4
2. x2 -5x 4x -20 x2 - x -20
3. x2 -5x 5x -25 x2 25
4. 2c2 -5x - 6x 15 2c2 -11x 15
5. 4w2 -6w 6w -9 4w2 - 9

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)

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Ex. 1 Find (y 5)(y 7)

• (y 5)(y 7) y y y 7 5 y 5 7
• y2 7y 5y 36
• y2 12y 36

Ex. 2 Find (3x - 5)(5x 2)
(3x - 5)(5x 2) 3x 5x 3x 2 -5 5x
-5 2 15x2 6x 25x - 10
15x2 - 19y - 10
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Ex. 3 Find (2x - 5)(3x2 -5x 4)

• (2x - 5)(3x2 -5x 4) 2x(3x2 -5x 4) 5(3x2
  -5x 4)
• 6x3 - 10x2 8x - 15x2 25x -20
• 6x3 (10 15)x2 (825)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
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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
2x4 - 9x3 10x2 - 57x 54