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How do you read and write equivalent expressions using
variables and exponents?
For example, what equivalent expression could represent x + x + x?
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In this lesson you will learn how to read and write
equivalent expressions by using variables and exponents.
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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
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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
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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
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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
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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)
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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.
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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
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In this lesson you have learned how to read and write
equivalent expressions by using variables and exponents.
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Let’s ReviewGuided Practice
Write two equivalent expressions for ten times the quantity of a number squared plus three.
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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)
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Let’s ReviewQuick Quiz
Write an equivalent expression for 2(a + 2).
Write an equivalent expression for 2x2 + 5.