Beginning Algebra, 11th Edition

SECTION 5.6 Special Products^337

Finding the Product of the Sum and Difference of Two Terms

Find each product.

(a)

Use the rule for the product of the sum and difference of two terms.

Apply the exponents.

(b)

= 16 x^2 - y^2

= 14 x 22 - y^2

14 x+ y 214 x-y 2

= 25 m^2 - 9

= 15 m 22 - 32 1 x+y 21 x-y 2 =x^2 - y^2

15 m+ 3215 m- 32

15 m+ 3215 m- 32

1 x + y 2 1 x - y 2

NOW TRY EXAMPLE 4

EXERCISE 4
Find each product.

(a)

(b)

(c)y 13 y+ 1213 y- 12

A 5 r-^45 BA 5 r+^45 B

14 x- 6214 x+ 62

NOW TRY
EXERCISE 5
Find the product.

12 m- 123

NOW TRY ANSWERS

4. (a)
   (b)
   (c) 9 y^3 - y

25 r^2 -^1625

16 x^2 - 36

(c)

= z^2 -

1

16

az-

1

4

baz+

1

4

b

(d)

Distributive property NOW TRY

OBJECTIVE 3 Find greater powers of binomials.The methods used in the

previous section and this section can be combined to find greater powers of binomials.

Finding Greater Powers of Binomials

Find each product.

(a)

Square the binomial.

Multiply polynomials.

Combine like terms.

(b)

Square each binomial.

Multiply polynomials.

Combine like terms.

(c)

Square the binomial.

Multiply polynomials.

Combine like terms.

=- 2 r^4 - 12 r^3 - 24 r^2 - 16 r Multiply. NOW TRY

=- 2 r 1 r^3 + 6 r^2 + 12 r+ 82

=- 2 r 1 r^3 + 4 r^2 + 4 r+ 2 r^2 + 8 r + 82

=- 2 r 1 r + 221 r^2 + 4 r+ 42

=- 2 r 1 r + 221 r+ 222 a^3 =a#a^2

- 2 r 1 r+ 223

= 16 y^4 - 96 y^3 + 216 y^2 - 216 y+ 81

- 108 y+ 36 y^2 - 108 y+ 81

= 16 y^4 - 48 y^3 + 36 y^2 - 48 y^3 + 144 y^2

= 14 y^2 - 12 y+ 9214 y^2 - 12 y+ 92

= 12 y- 32212 y- 322 a^4 =a^2 #a^2

12 y- 324

= x^3 + 15 x^2 + 75 x+ 125

= x^3 + 10 x^2 + 25 x+ 5 x^2 + 50 x+ 125

= 1 x^2 + 10 x+ 2521 x+ 52

= 1 x+ 5221 x+ 52 a^3 =a^2 #a

1 x+ 523

EXAMPLE 5

= 4 p^3 - p

= p 14 p^2 - 12

p 12 p+ 1212 p- 12

5. 8 m^3 - 12 m^2 + 6 m- 1