Algebra 1 Common Core Student Edition, Grade 8-9

@ Common Core State Standards

KA \ /in n A -AP R.A .1 Understand that polynomials form a

/VlUiripiyiriU system analogous to the integers, namely, they are

* I closed under the operations of addition, subtraction, and

Q I /~l I [ /''I ppr multiplication; add, subtract, and multiply polynomials.

MP 1, MP 2, MP 3, MP 4, MP 7, MP 8

Objectives To find the square of a binom ial an d to find th e p ro d u ct of a sum an d difference

Getting Ready!

Yo u a r e m ak i n g sq u ar e i n v i t at i o n s f o r a p a r t y.

Yo u s t a r t w i t h a sq u ar e p i ece o f p ap er w i t h

6 -in. sides. You reduce both its length and

its width by x, as shown. W hat is the area of

How is th is Solve the invitation? Justify your reasoning.

It like the one for

Lesson 8-3? How is

it d iffe re n t?

MATHEMATICAL

I P R A C T I C E S

Essent ial Und er st and ing There are special rules you can use to simplify the

square of a binom ial or th e p ro d u c t of a sum an d difference.

Squares of binom ials have th e form (a + b)2 or (a - b)2. You can algebraically

simplify the p ro d u c t or you can u se an area m odel to discover th e rule for simplifying

(a + b)2, as shown below.

Simplify the product.

(a + b)2 = {a + b)[a + b)

= a2 + ab + ba + b2 Multiply the binomials.

= a2 + 2 ab + b2 Simplify.

Area Model

a2 + lab + b2

Key Concept The Square of a Binomial

Words The square of a binom ial is th e square of th e first term plus twice th e p ro d u c t of

th e two term s plus th e square of the last term.

Algebra Examples

{a + b)2 = a2^ +^2 ab^ + b2 (x + 4)2 = x2 + 8x + 16

(a - b)2 = a2 - 2ab + b2 (x - 3)2 = x2 - 6x + 9

504 Chapter 8 Polynomials and Factoring