McGraw-Hill Education GRE 2019

Simplifying Expressions

Before you dive into the process for solving for a variable, let’s review ways to

simplify expressions. An expression is some combination of variables, values, or

both. Examples of expressions are 3x + 7,^2 yx, 9z^3.

When presented with an expression, either by itself or as part of an equation,

your first step should always be to simplify the expression. Generally, there are

three ways to do so:

Combine Like Terms

Simplify: 3 x + 5z + 9x − 2z.

SOLUTION: Combine the xs and arrive at 12x. Combine the zs and arrive at 3z.

The expression simplifies to 12x + 3z.

Simplify: 2(x+3) + 3(x + 3).

SOLUTION: Think of (x +3) as a variable, such as z. 2z + 3z = 5z. Therefore,

2(x + 3) + 3(x + 3) = 5(x + 3).

Find a Common Denominator

Simplify: 53 a +^25 b.

SOLUTION: Find a common denominator of 15 for both terms.

53 a ×^55 =^2515 a

25 b ×^33 =^615 b

↓

2515 a +^615 b =^25 a + 156 b

Simplify: (^7) x −^3 y.
SOLUTION: Find a common denominator of xy for both terms.
(^7) x × yy = xy^7 y
(^3) y × xx =^3 xyx
↓
(^7) xyy −^3 xyx =^7 y – xy^3 x
CHAPTER 11 ■ ALGEBRA 259
03-GRE-Test-2018_173-312.indd 259 12/05/17 11:53 am