McGraw-Hill Education GRE 2019

When you have the opportunity to factor or use FOIL on the GRE, it’s

usually a good idea to do so!

Common Quadratics

Three quadratic expressions appear so frequently on the GRE that it is worth

memorizing their structure instead of factoring or using FOIL each time you

encounter them:

1. (x + y)(x − y) = x^2 − y^2


2. (x + y)(x + y) = (x + y)^2 = x^2 + 2xy + y^2


3. (x − y)(x − y) = (x − y)^2 = x^2 − 2xy + y^2

Memorizing the preceding formulas is useful for a couple of reasons:

■ If you know the forms of these expressions after applying FOIL and after

factoring, you will be able to save time when you encounter their general

form on the GRE.

■ Often, the GRE will put these expressions in an unorthodox form. In these

cases, you will need to recognize that an unusual-seeming expression is

actually one of the common quadratics.

For example, (√ 7 + √ 3 )(√ 7 − √ 3 ) =?

Since you are multiplying two binomials, you might be tempted to distribute,

but notice that (√ 7 + √ 3 )(√ 7 − √ 3 ) is in the same form as (x + y)(x − y),

where √ 7 is x and √ 3 is y. From the first special product, you know that

(x + y)(x − y) = (x^2 − y^2 ). Therefore,

(√7 + √ 3 )(√ 7 − √ 3 )

= √ 7

2

• √ 3

2

= 7 − 3

= 4

286 PART 4 ■ MATH REVIEW

03-GRE-Test-2018_173-312.indd 286 12/05/17 11:55 am