- Interior Design A square green rug h as a blue square in th e center. The side length
of th e blue square is x inches. The w idth of th e green b a n d th a t su rro u n d s the blue
square is 6 in. W hat is the area of th e green band?
Q ApplyMental Math Simplify each product.- 612 21. 792 22.^482 23.^4032
See Problem 3.- 3022
Simplify each product.- (f + 6 )(i' - 6 )
- (x - 3)(x + 3)
26. (b + l)(b - 1)
29. (10 + y)(10 — y)
See Problem 4.- (z - 5)(z + 5)
- (t - 13)(t + 13)
Mental Math Simplify each product.- 42 • 38 32. 79 • 81 33. 63 • 57 34. 399 • 401
^ See Problem 5.- 303 • 297
Simplify each product.- (m + 3ri)2
- (9k + 2 q)2
- (4x + 7y)(4x - 7y)
- (r 2 + 3s)(r2 - 3s)
- (2a + bf 38. (4s - t)2
- (8r — 5s)2 42. (s + 6f2)2
- (a - 6 b){a + 6b)
- (2p2 + 7q){2p2 - 7q)
- (g — 7h)2
- (p 4 - 9q2)2
- (2g + 9h)(2g - 9h)
- (3w3 - z2)(3w3 + z 2)
- Error Analysis D escribe an d correct th e error m ad e in simplifying th e product.
5 1. T h in k A b o u t a Plan A com pany logo is a w hite square inside a red square. The side
length of th e w hite square is x + 2. The side length of th e red square is three tim es
th e side length of th e w hite square. W hat is th e area of the red p art of the logo?
W rite your answ er in stan d ard form.- How can drawing a diagram help you solve th e problem?
- How can you express th e area of th e red p art of the logo as a difference of areas?
- Construction A square deck has a side length of x + 5. You are expanding th e deck
so th at each side is four tim es as long as th e side length of th e original deck. W hat is
th e area of the new deck? W rite your answ er in stan d ard form. - Reasoning Use th e area m odel at the right to write a second
expression for th e area of th e square labeled (a - b)2. Then simplify
th e expression to derive th e rule for th e square of a binom ial of the
form a — b. - Open-Ended Give a counterexam ple to show th at
(x + y)2 = x 2 + y 2 is false.
(^55) Reasoning Does ( 3 ^ j 2 = 9 |? Explain.
a - b
508 Chapter 8 Po l y n o m i al s an d Fact o r in g