holt algebra 1 7-7 multiplying polynomials warm up evaluate. 1. 3 2 3. 10 2 simplify. 4. 2 3 2 4 6....
TRANSCRIPT
Holt Algebra 1
7-7 Multiplying Polynomials
Warm UpEvaluate.
1. 32
3. 102
Simplify.
4. 23 24
6. (53)2
9 16
100
27
2. 24
5. y5 y4
56 7. (x2)4
8. –4(x – 7) –4x + 28
y9
x8
Holt Algebra 1
7-7 Multiplying Polynomials
Students will be able to: Multiply polynomials.
Learning Target
Holt Algebra 1
7-7 Multiplying Polynomials
To multiply polynomials, you will use some of the properties of exponents that you learned earlier in this chapter.
Holt Algebra 1
7-7 Multiplying Polynomials
Multiply.
A. (6y3)(3y5)
=18y8
B. (3mn2) (9m2n)
=27m3n3
Holt Algebra 1
7-7 Multiplying Polynomials
Multiply.
2 2 2112
4s t st st
4 53s t(2r2t)(5t3)
10r2t4
2112
3x y x z y z
2 4 53
7554x y z
Holt Algebra 1
7-7 Multiplying Polynomials
Multiply.
4(3x2 + 4x – 8)
12x2 + 16x – 32
(6pq)(2p – q)
12p2q – 6pq2
Holt Algebra 1
7-7 Multiplying Polynomials
Multiply.
x y 22 612
xyyx 8 2
3x3y2 + 4x4y3
2(4x2 + x + 3)
8x2 + 2x + 6
3ab(5a2 + b)
15a3b + 3ab2
5r2s2(r – 3s)
5r3s2 – 15r2s3
Holt Algebra 1
7-7 Multiplying Polynomials
To multiply a binomial by a binomial, you can FOIL:
3 2x x
FOIL
2 2 3 6x x x 2 5 6x x
Holt Algebra 1
7-7 Multiplying Polynomials
Multiply.
(s + 4)(s – 2)
4 2s s
FOIL
2 2 4 8s s s 2 2 8s s
Holt Algebra 1
7-7 Multiplying Polynomials
In the expression (x + 5)2, the base is (x + 5). (x + 5)2 = (x + 5)(x + 5)
Helpful Hint
Holt Algebra 1
7-7 Multiplying Polynomials
Multiply.
(x – 4)2
4 4x x
FOIL
2 4 4 16x x x 2 8 16x x
Holt Algebra 1
7-7 Multiplying Polynomials
Multiply.
(8m2 – n)(m2 – 3n)
8m4 – 24m2n – m2n + 3n2
8m4 – 25m2n + 3n2
Holt Algebra 1
7-7 Multiplying Polynomials
Multiply.
(x – 3)2
3 3x x
FOIL
2 3 3 9x x x 2 6 9x x
Holt Algebra 1
7-7 Multiplying Polynomials
Multiply.
(2a – b2)(a + 4b2)
2 22 4a b a b
FOIL
2 2 2 42 8 4a ab ab b 2 2 42 7 4a ab b
Holt Algebra 1
7-7 Multiplying Polynomials
To multiply polynomials with more than two terms, you can use the Distributive Property several times. Multiply (5x + 3) by (2x2 + 10x – 6):
(5x + 3)(2x2 + 10x – 6)
2
3
2
2
310 50 30 6 30 18
10 56 18
x x x x x
x x
Holt Algebra 1
7-7 Multiplying Polynomials
We can use generic rectangles as area models to
find the products of polynomials. A generic rectangle
helps us organize the problem. It does not have to be
drawn accurately or to scale.
2Multiply 9 3 5x x x
2x 3x
x
93x 23x
29x 27x
3 26 22 45x x x
5
5x
45
Holt Algebra 1
7-7 Multiplying Polynomials
Multiply.(x – 5)(x2 + 4x – 6)
2x 4x
x
53x 24x
25x 20x
66x
30
3 2 26 30x x x
Holt Algebra 1
7-7 Multiplying Polynomials
Multiply.(2x – 5)(–4x2 – 10x + 3)
24x 10x2x
538x 220x
220x 50x
3
6x
15
38 56 15x x
Holt Algebra 1
7-7 Multiplying Polynomials
Multiply.
(x + 3)3 3 3 3x x x
3 3x x
FOIL
2 3 3 9x x x 2 6 9x x
2x 6x
x
33x 26x
23x 18x
9
9x
27
3 29 27 27x x x
Holt Algebra 1
7-7 Multiplying Polynomials
Multiply.(3x + 1)(x3 – 4x2 – 7)
3x 24x
3x
143x 312x
3x 24x
721x
7
4 3 23 11 4 21 7x x x x
Holt Algebra 1
7-7 Multiplying Polynomials
Multiply.
(x + 3)(x2 – 4x + 6)
2x 4x
x
33x 24x
23x 12x
6
6x
18
3 2 6 18x x x
Holt Algebra 1
7-7 Multiplying Polynomials
The length of a rectangle is 4 meters shorter than its width.
a. Write a polynomial that represents the area of the rectangle.
A l w w
4w 4w w 2 4w w
Holt Algebra 1
7-7 Multiplying Polynomials
The length of a rectangle is 4 meters shorter than its width.
b. Find the area of a rectangle when the width is 6 meters.
w
4w
2 4A w w w 2
2
6 6 4 6
36 24
12 m
A
HW Pages 497-499/27-69 Odd, 75-84, 87-89