Algebra 1 Common Core Student Edition, Grade 8-9

Factoring

Special Cases

Common Core State Standards

A-SSE.A.1a Interpret parts of an expression, such

as terms, factors, and coefficients. Also A-SSE.A.1b,

M ACC.912.A-SSE.A.2

MP 1, MP 2, MP 3, MP 4

Objective To factor perfect-square trinomials and the differences of two squares

Get t i n g Read y!

Start with a pi

What do you need

to find out about

each square first?

The diagram shows two ad jacent

sq u ar es and t h ei r ar e a s. I n t er m s

of x, how much t aller is the left

sq u ar e t h an t h e r i g h t sq u ar e?

Ex p l a i n y o u r r e a so n i n g.

MATHEMAIICAL

PRA CTICES

14x + 49

Esse n t i a l U n d e r st a n d i n g You can factor some trinomials by “reversing” the

rules for multiplying special case binomials that you learned in Lesson 8-4.

Lesso n
Vocabulary
perfect-square
trin om ial
difference of
tw o squares

For example, recall the rules for finding squares of binomials.

(a + b)2 = (a + b)[a + b) = a2 + 2 ab + b2

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

Any trinomial of the form a2 + 2ab + b2 or a2 - 2ab + b2 is a perfect-square trinomial

because it is the result of squaring a binomial. Reading the equations above from right

to left gives you rules for factoring perfect-square trinomials.

Key Concept Factoring Perfect-Square Trinomials

,

Algebra For every real number a and b:

a2 + 2 ab + b2 = (a +b)(a + b) = (a+ b)2

a2 - 2 ab + b 2 = (a -b)(a — b ) = ( a — b)2

Examples x2 + 8x + 16 = (x + 4)(x + 4) = (x + 4)2

4n2 — 12 n + 9 = (2 n- 3)(2n - 3) = (2n - 3)2

Y J

Here is how to recognize a perfect-square trinomial:

• The first and the last terms are perfect squares.


• The middle term is twice the product of one factor from the first term and one
  factor from the last term.

PowerAlgebra.com I Lesson 8-7 Fact oring Special Cases 523