Easy Algebra Step-by-Step

134 Easy Algebra Step-by-Step

b. x^2 + 6 x+ 9

Step 1. Identify the coeffi cients a, b, and c and check whether bac.

a= 1, b= 6, and c= 9

|b| = |6| = 6 and 22 ac 2 ⋅ 199 = 211 ⋅ 36

Thus, x^2 + 6 x+ 9 is a perfect trinomial square.

Step 2. Indicate that x^2 + 6 x + 9 will factor as the square of a binomial.

x^2 + 6 x + 9 = ( )^2

Step 3. Fill in the binomial. The fi rst term is the square root of x^2 and the

last term is the square root of 9. The sign in the middle is the same

as the sign of the middle term of the trinomial.

xx^2 + 696 xx =()+^2 is the factored form.

Factoring Two Terms

When you have two terms to factor, consider these special binomial products

from Chapter 9: the difference of two squares, the difference of two cubes,

and the sum of two cubes.

The difference of two squares has the

form x^2 − y^2 (quantity squared minus quan-

tity squared). You factor the difference of two

squares like this:

x^2 −y^2 = (x+y)(x−y)

The difference of two cubes has the form x^3 − y^3 (quantity cubed minus

quantity cubed). You factor the difference of two cubes like this:

x^3 − y^3 = (x − y)(x^2 + xy + y^2 )

The sum of two cubes has the form x^3 +y^3 (quantity cubed plus quantity

cubed). You factor the sum of two cubes like this:

x^3 + y^3 = (x + y)(x^2 − xy + y^2 )

Problem Factor.

a. 9 x^2 − 25 y^2

b. x^2 − 1

x^2 + y^2 , the sum of two squares, is not

factorable (over the real numbers).