How do you read and write equivalent expressions using

variables and exponents?

For example, what equivalent expression could represent x + x + x?

In this lesson you will learn how to read and write

equivalent expressions by using variables and exponents.

Let’s ReviewLet’s Review

We know that algebraic expressions contain numbers, operations and at

least one variable. 2(x + 3)

4a-3 15 ÷ y

12 - w2

Let’s ReviewLet’s Review

Exponents show how many times the base number is used as a factor.

42

exponent

base

42 is equivalent to 4 • 4

Let’s ReviewLet’s Review

Parentheses can be used to show a part of an expression that needs to be done first.

5(x + 2) - 6

Let’s ReviewA Common Mistake

Multiplying the base number by the exponent

42

42 ≠ 4 • 2

exponent

base

42 is not equivalent to 4 • 2

Let’s ReviewCore Lesson

Let’s look at the expression x + x + x for x = 4.

x + x + x 4 + 4 + 4

2x + x 2(4)+ 4

3x 3(4)

Let’s ReviewCore Lesson

Let’s write an equivalent algebraic expression for x times x plus 3.

x • x + 3Since “x” is used as a factor two

times, we can write x2.

x2 + 3

So, an equivalent

expression for x• x + 3 is

x2 + 3.

Let’s ReviewCore Lesson

How could we write the algebraic expression for two times the quantity of x2 plus x?

2(x2 + x) is the same as (x2 + x) + (x2 + x) or x2 + x + x2 + x

factor times 2

In this lesson you have learned how to read and write

equivalent expressions by using variables and exponents.

Let’s ReviewGuided Practice

Write two equivalent expressions for ten times the quantity of a number squared plus three.

Let’s ReviewExtension Activities

Write an equivalent expression for each of the following:

a. x + 1 + xb. y + y + y + yc. 2x2

d. 3(y + 5)

Let’s ReviewQuick Quiz

Write an equivalent expression for 2(a + 2).

Write an equivalent expression for 2x2 + 5.