Warm Up

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Preview
Warm Up
California Standards
Lesson Presentation
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Warm Up Simplify.
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1. 9 13 ? 5 3
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2. 16 ? 8 4 ? 1
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3. 6 9 ? 10 3
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4. 17 8 ? 20 ? 2
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Vocabulary
term like term coefficient constant equivalent
expression
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In the expression below, 7x, 5, 3y, and 2x are
terms. A term can be a number, a variable, or a
product of numbers and variables. Terms in an
expression are separated by plus or minus signs.
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Like terms, such as 7x and 2x, can be grouped
together because they have the same variable
raised to the same power. Often, like terms have
different coefficients. A coefficient is a number
that is multiplied by a variable in an algebraic
expression. A constant is a number that does not
change. Constants, such as 4, 0.75, and 11, are
also like terms.
When you combine like terms, you change the way
an expression looks but not the value of the
expression. Equivalent expressions have the same
value for all values of the variables.
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Additional Example 1 Combining Like Terms in
One-Variable Expressions
Combine like terms.
A. 14a 5a
Identify like terms.
9a
Combine coefficients 14 5 9
Identify like terms the coefficient of y is 1,
because 1y y.
B. 7y 8 3y 1 y
Combine coefficients 7 3 1 5 and 8 1 7
5y 7
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Check It Out! Example 1
Combine like terms.
Identify like terms the coefficient of q is 1,
because 1q q.
A. 4q q
3q
Combine coefficients 4 1 3
Identify like terms the coefficient of c is 1,
because 1c c.
B. 5c 8 4c 2 c
Combine coefficients 5 4 1 0 and 8 2 6
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Additional Example 2A Combining Like Terms in
Two-Variables Expressions
Combine like terms.
9x 3y 2x 5
9x 3y 2x 5
Identify like terms.
7x 3y 5
Combine coefficients 9 2 7
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Additional Example 2B Combining Like Terms in
Two-Variable Expressions
Combine like terms.
5t 7p 3p 2t
5t 7p 3p 2t
Identify like terms.
Combine coefficients 5 2 3 and 7 3 4
3t 4p
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Additional Example 2C Combining Like Terms in
Two-Variable Expressions
Combine like terms.
4m 9n 2
4m 9n 2
No like terms.
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Check It Out! Example 2
Combine like terms.
A. 2x 5x 4y 3
2x 5x 4y 3
Identify like terms.
Combine coefficients 2 5 7
7x 4y 3
B. 9d 7c 4d 2c
9d 7c 4d 2c
Identify like terms.
5d 5c
Combine coefficients 9 4 5 and 7 2 5
C. 8g c 6
8g c 6
No like terms.
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To simplify an expression, perform all possible
operations, including combining like terms. You
may need to use the Associative, Commutative, or
Distributive Properties.
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Additional Example 3 Using the Distributive
Property to Simplify
Simplify 6(5 n) 2n.
6(5 n) 2n
6(5) 6(n) 2n
Distributive Property
30 6n 2n
Multiply.
30 6n 2n
Identify like terms.
30 4n
Combine coefficients 6 2 4.
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Check It Out! Example 3
Simplify 3(c 7) c.
3(c 7) c
3(c) 3(7) c
Distributive Property
3c 21 c
Multiply.
3c 21 c
Identify like terms.
2c 21
Combine coefficients 3 1 2.
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Lesson Quiz
Combine like terms. 1. 3x 4 2x 2. 13k 6
? 8m 9 k Simplify. 3. 4(3x 6) ? 7x 4.
6(x 5) 3x Solve. 5. The accounting
department ordered 15 boxes of pens. The
marketing department ordered 9 boxes of pens. If
the total cost of the combined order was 72,
what is the price of each box of pens?
5x 4
14k 8m 15
5x 24
9x 30
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