Compact form:
Add.(b)
First Outer Inner LastCombine like terms.(c)
FOIL
Combine like terms. NOW TRYOBJECTIVE 4 Find the product of the sum and difference of two terms.
The product of the sum and difference of the same two terms occurs frequently.
FOIL=x^2 - y^2 Combine like terms.
=x^2 - xy+ xy- y^2
1 x+ y 21 x- y 2
= 10 k^2 + 9 kz- 9 z^2
= 10 k^2 - 6 kz+ 15 kz- 9 z^2
12 k+ 3 z 215 k- 3 z 2
= 18 a^2 + 9 ab- 20 b^2
= 18 a^2 + 24 ab- 15 ab- 20 b^2
16 a- 5 b 213 a+ 4 b 2
- 11 m
4 m- 15 m
14 m- 5213 m+ 12 = 12 m^2 - 11 m- 5
12 m^2 - 5296 CHAPTER 5 Exponents, Polynomials, and Polynomial Functions
Product of the Sum and Difference of Two TermsThe product of the sum and difference of the two terms xand yis the differ-
ence of the squares of the terms.
1 xy 21 xy 2 x^2 y^2
Multiplying the Sum and Difference of Two TermsFind each product.
EXAMPLE 5
(a) (b)
= 4 r^2 - 25
= 22 r^2 - 25
= 12 r 22 - 52
12 r+ 5212 r- 52
= p^2 - 49
=p^2 - 72
1 p+ 721 p- 72
(c) (d)
= 2 x^5 - 18 x^3 NOW TRY
= 2 x^31 x^2 - 92
2 x^31 x+ 321 x- 32
= 36 m^2 - 25 n^2
= 16 m 22 - 15 n 22
16 m+ 5 n 216 m- 5 n 2
OBJECTIVE 5 Find the square of a binomial.To find the square of a binomial
or multiply by itself.
FOIL
Combine like terms.A similar result is true for the square of a difference.
=x^2 + 2 xy+ y^2
=x^2 +xy+xy+y^2
1 x+ y 21 x+y 2
x+y, 1 x+ y 22 , x+ y
NOW TRY
EXERCISE 4
Use the FOIL method to find
the product.
13 p-k 215 p+ 4 k 2NOW TRY ANSWERS
4.
- (a) 9 x^2 - 49 y^2 (b) 20 k^3 - 45 k
15 p^2 + 7 k p- 4 k^2NOW TRY
EXERCISE 5
Find each product.
(a)
(b) 5 k 12 k- 3212 k+ 32
13 x- 7 y 213 x+ 7 y 2