Algebra 1 Common Core Student Edition, Grade 8-9

^ Got It? 3. a. W hat is 852? Use m en tal m ath.

b. Reasoning Is there m ore th a n one way to find 852 using m ental m ath?

Explain your reasoning.

The p ro d u c t of th e sum a n d difference of th e sam e two term s also p roduces a pattern.

(a + b){a - b) = a 2 - ab + ba — b2

= a2 - b 2

Notice that the sum

of -a b and ba is 0 ,

leaving a 2 - b2.

Key Concept The Product of a Sum and Difference

Words The p ro d u c t of th e sum a n d difference of th e sam e two term s is th e difference of

th eir squares.

Algebra Examples

{a + b){a - b) = a2 — b2 (x + 2)(x - 2) = x2 - 22 = x2 - 4

.Plan
How do you choose
w h ic h ru le t o use?
The firs t fa c to r in th e
p ro d u ct is th e sum o f x 3
and 8. T h e s e c o n d f a c t o r
is th e diffe re n ce o f x 3
and 8. So, u s e t h e r u l e f o r
th e p ro d u ct o f a sum and
difference.

Pr o b l em 4 Finding the Product of a Sum and Difference

W hat is a sim p le r fo rm o f (x 3 + 8 )(x 3 — 8)?

^Thjnk

Write the original product.

Identify w hich terms

correspond to a and b in the

ru le fo r th e p ro d u c t o f a sum

and difference.

Substitute for a and b in

th e rule.

Simplify.

write

(x 3 + 8 )(x 3 - 8 )

a = x 3; b = 8

(x 3 + 8 )(x 3 - 8 ) = ( x3)2 - (8)2

= x 6 - 64

0 G ot It? 4. W hat is a sim pler form of each product?

a. (x + 9)(x - 9) b. (6 + m2)(6 - m2) c. (3c - 4)(3c + 4)

5 0 6 Chapter 8 Polynomials and Factoring