Algebra 1 Common Core Student Edition, Grade 8-9

W hen you use th e D istributive P roperty to m ultiply binom ials, notice th a t you m ultiply

each term of the first binom ial by each term of th e seco n d binom ial. A table can help

you organize your work.

Think
Is th is th e o n ly ta b le
you can make?
No. You can w rite th e
terms o f x - 3 in a ro w
and the terms o f 4x - 5
in a colum n.

Usi ng a Tabl e

W hat is a sim p le r fo rm o f (x - 3)(4x - 5)?

Binomial factors Product of binomials

written in standard

form

Use a table.

Make a table of products.

4x -5

X 4x2 -5 x

-3 -1 2 x^15

When labeling the rows

and columns, th ink of

x - 3 a s * + ( - 3 ). Think

o f 4x - 5 as 4x + ( - 5 ).

The p ro d u c t is 4x2 — 5x — 12x + 15, or 4x2 — 17x + 15.

& Got It? 2. W hat is a sim pler form of (3x + l)(x + 4)? Use a table.

Sar

There is a sh o rtcu t you can use to m ultiply two binom ials. C onsider th e p ro d u ct of

2x + 2 and x + 3. The large rectangle below m odels this product. You can divide the

large rectangle into four sm aller rectangles.

The area of th e large rectangle is th e sum of th e areas of th e four sm aller rectangles.

I- 2 x + 2 ---------

x + 3

2x 2

X

------------

2x2 2x

3 6x 6

2x I

(2x + 2)(x + 3) = (2x)(x) + (2x)(3) + (2)(x) + (2)(3)

= 2x

= 2x2

+

+

6x

8x

+

' +

2x

6

The area o f each rectangle is the

product of one term of 2x + 2

and one term of x + 3.

This m odel illustrates a n o th er way to find th e p ro d u c t of two binom ials. You find the

sum of the p roducts of the First term s, th e O uter term s, th e In n e r term s, a n d th e Last

term s of th e binom ials. The acronym FOIL m ay help you re m e m b er this m ethod.

PowerAlgebra.com Lesson 8-3 Multiplying Binomials 499