Algebra 1 Common Core Student Edition, Grade 8-9

@ Common Core State Standards

K.A Rirt/ -\rY"»I/ -ilc A -AP R.A .1 Understand that polynomials form a

/V \U III piyillQ D I nom I U 15 system analogous to the integers, namely, they are

1 ' ^ closed under the operations of addition, subtraction, and

multiplication; add, subtract, and multiply polynomials.

M P 1, M P 2, M P 3, M P 4, M P 7, M P 8

Objective To m ultiply two binom ials or a binom ial by a trinom ial

Y o u've g o t a

diagram. How

can you use it to

create expressions

fo r the width and

fo r the length?

Get t i n g Read y!

A park has a rectangular dog run with length 30 ft

an d w i d t h 2 0 f t. T h e p ar k s d ep ar t m en t w an t s t o

expand each end o f each sid e o f t h e dog run by

the same amount x. What will be the total area of

the expanded dog run? Justify your reasoning.

X

X

20

X 30 ft

X

mathematical Essent ial Und er st and ing There are several ways to find th e p ro d u c t of two

PRACTICES binomials, including models, algebra, and tables.

O ne way to find th e p ro d u c t of two binom ials is to u se a n area m odel, as show n below.

This m odel shows

th a t ( 2 x + 1 )(x + 2 )

can be w ritte n in

standard form as

2x 2 + 5x + 2.

You can also use th e D istributive P roperty to find th e p ro d u c t of two binom ials.

X2 X2

XX 1

XX 1

x + 2

• 2 x + 1

,
Is th e p ro d u c t o f tw o
polynomials always
a polynom ial?
Yes. The set o f polynom ials
is dosed under
multiplication, which
means that multiplying
polynom ials always gives
you a n o ther polynom ial.

Using the Distributive Propert y

W hat is a sim p le r fo rm o f (2x + 4)(3x - 7)?

(2x + 4)(3x - 7) = 2x(3x - 7) + 4(3x - 7)

= 6x2 - 14x + 4(3x - 7)

= 6x 14x + 12x - 28

= 6x2 - 2x - 28

Go t I t?

Distribute the second factor, 3x - 7.

Distribute 2x.

Distribute 4.

Combine like terms.

1. W hat is a sim pler form of (x - 6)(4x + 3)?

Ch ap t er 8 Pol yn om i al s and Factoring