7-7 Multiplying Polynomials
Warm Up
Evaluate.
1. 32
2. 24 16
9
3. 102 100
Simplify.
4. 23  24 27
5. y5  y4 y9
6. (53)2
7. (x2)4
56
8. –4(x – 7)
Holt Algebra 1
–4x + 28
x8
7-7 Multiplying Polynomials
Learning Target
Students will be able to: Multiply
polynomials.
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.

(2r2t)(5t3)

Holt Algebra 1
10r2t4
1 2 
3 2
4 5
x
y
12
x z  y z



3


4x 5y 5 z 7

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.
1 2
2 2
xy
x y 6
+ 8x y
2


3ab(5a2 + b)
3x3y2 + 4x4y3
15a3b + 3ab2
2(4x2
5r2s2(r – 3s)
8x2
+ x + 3)
+ 2x + 6
Holt Algebra 1
5r3s2 – 15r2s3
7-7 Multiplying Polynomials
To multiply a binomial by a binomial, you can
FOIL:
FOIL
 x + 3 x + 2
x + 2 x + 3x + 6
2
x + 5x + 6
2
Holt Algebra 1
7-7 Multiplying Polynomials
Multiply.
(s + 4)(s – 2)
FOIL
 s + 4 s  2
s  2s + 4s  8
2
s + 2s  8
2
Holt Algebra 1
7-7 Multiplying Polynomials
Helpful Hint
In the expression (x + 5)2, the base is (x + 5).
(x + 5)2 = (x + 5)(x + 5)
Holt Algebra 1
7-7 Multiplying Polynomials
Multiply.
(x – 4)2
FOIL
 x  4 x  4
x  4 x  4 x + 16
2
x  8x + 16
2
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
FOIL
 x  3 x  3
x  3x  3x + 9
2
x  6x + 9
2
Holt Algebra 1
7-7 Multiplying Polynomials
Multiply.
(2a – b2)(a + 4b2)
FOIL
 2a  b  a + 4b 
2
2
2a + 8ab  ab  4b
2
2
2
2a + 7ab  4b
2
Holt Algebra 1
2
4
4
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)
 10 x + 50 x  30 x + 6 x + 30 x  18
3
2
 10 x + 56 x  18
3
Holt Algebra 1
2
2
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.
Multiply
2
3
2
x
+
9
x

3
x
+
5


  x + 6x  22x + 45
9 9x 227 x 45
x x3 3x 2 5x
x 2 3x 5
Holt Algebra 1
7-7 Multiplying Polynomials
Multiply.
(x – 5)(x2 + 4x – 6)
5 5x 220x 30
x x3 4x 2 6x
x 2 4x 6
 x  x  26 x + 30
3
Holt Algebra 1
2
7-7 Multiplying Polynomials
Multiply.
(2x – 5)(–4x2 – 10x + 3)
5 20x 2 50x 15
3
2

8x
6x

20x
2x
2
10x 3
4x
 8x + 56 x  15
3
Holt Algebra 1
7-7 Multiplying Polynomials
Multiply.
(x + 3)3
  x + 3 x + 3 x + 3
FOIL
 x + 3 x + 3
x + 3x + 3x + 9
3 3x 2 18x 27
x x3 6x 2 9x
x 2 6x
9
2
x + 6x + 9
2
Holt Algebra 1
 x + 9 x + 27 x + 27
3
2
7-7 Multiplying Polynomials
Multiply.
(3x + 1)(x3 – 4x2 – 7)
1 x3 4x 2 7
4
3
3x

21x

12x
3x
x3 4x 2 7
 3x  11x  4 x  21x  7
4
Holt Algebra 1
3
2
7-7 Multiplying Polynomials
Multiply.
(x + 3)(x2 – 4x + 6)
3 3x 2 12x 18
x x3 4x 2 6x
x 2 4x 6
 x  x  6 x + 18
3
Holt Algebra 1
2
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  4 w
2
 w  4w
Holt Algebra 1
w
w4
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.
A w  w  4w
2
A 6  6  4 6
2
 36  24
 12 m
2
HW Pages 497-499/27-69 Odd, 75-84, 87-89
Holt Algebra 1
w
w4