Algebra 1 Common Core Student Edition, Grade 8-9

|P [a n
What rule can you
use to sim plify this
product?
(2m - 3)2 may not look
like (a - b)2, b u t it has
th e same fo rm. Use th e
rule fo r (a - b)2 and let
a = 2m and b = 3.

Pl an

How do you find the

area of the walkway?

The area o f th e w a lk w a y

is th e diffe re n ce o f th e

total area and the area of

the patio.

Thin k

What number close

to 39 can you square

mentally?

The nearest m u ltip le o f

10 to 39 is 40, w h ic h is

a n u m ber you should be

able to square mentally.

Sq u a r i n g a Bi n o m i al

What is a simpler form of each product?

Q(x + 8)2 = x 2 + 2x(8) + 82 Square the binom ial.

= x 2 + 16x+64 Simplify.

0 (2m - 3)2 = (2m)2 - 2(2m)(3) + 3 Square the binom ial.

= 4m2 - 12m + 9 Simplify.

& Got It? 1. W hat is a sim pler form of each product?

a. {n - 7)2 b. (2x + 9)2

Applying Squares of Binomials

Exterior Design A square outdoor patio is surrounded by a

brick walkway as shown. What is the area of the walkway?

Step 1 Find the total area of th e patio a n d walkway.

(x + 6)2 = x 2 + 2 (x)(6 ) + 62 Square the binomial. ^x

= x 2 + 1 2 x + 3 6 Simplify.

S te p 2 Find the area of th e patio.

The area of th e patio is x • x, or x2.

Step 3 Find the area of th e walkway.

Area of walkway = Total area - Area of patio

= (x 2 + 12x + 36) - x 2 Substitute.

= (x 2 - x 2) + 12x + 36 Group like terms.

= 12x+36 Simplify.

The area of th e walkway is (1 2 x + 36) ft2.

Go t I t? 2. In Problem 2, su ppose th e brick walkway is 4 ft wide. W hat is its area?

Using m ental m ath, you can square a binom ial to find th e square of a num ber.

Usi ng M ent al M at h

What is 392? Use mental math.

392 = (40 - l)2 Write 39 2 as th e s q u a re o f a b in o m ia l.

= 4 0 2 - 2 ( 4 0 ) ( 1 ) + l 2 Square the binomial.

= 1 6 0 0 - 8 0 + 1 S im p lify.

= 1521 Simplify.

| Lesso n f M Multiplying Special Cases 505

c

PowerAlgebra.com