SIMPLIFIED EXPRESSIONS The distributive property allows you to combine
like terms by adding their coefficients. An expression is simplified if it has no
grouping symbols and if all the like terms have been combined.
EXAMPLE
Student Help
2
Combine Like Terms
Simplify the expression.
STUDY TIP
In Example 2 the
distributive property
has been extended to
three terms:
(b c d)a ba ca da
a. 8x 3x
b. 2y2 7y2 y2 2
Solution
a. 8x 3x (8 3)x
Use distributive property.
11x
Add coefficients.
b. 2y2 7y2 y2 2 2y2 7y2 1y2 2
EXAMPLE
Student Help
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INT
(2 7 1)y2 2
Use distributive property.
8y2 2
Add coefficients.
Simplify Expressions with Grouping Symbols
Simplify the expression.
MORE EXAMPLES
NE
ER T
3
Coefficient of y 2 is 1.
a. 8 2(x 4)
b. 2(x 3) 3(5 x)
Solution
a. 8 2(x 4)
8 2(x) (2)(4)
Use distributive property.
8 2x 8
Multiply.
2x 8 8
Group like terms.
2x
Combine like terms.
b. 2(x 3) 3(5 x)
2(x) 2(3) 3(5) 3(x)
Use distributive property.
2x 6 15 3x
Multiply.
2x 3x 6 15
Group like terms.
x 21
Combine like terms.
Simplify Expressions
Simplify the expression.
108
Chapter 2
3. 5x 2x
4. 8m m 3m 5
5. x 2 5x x 2
6. 3(y 2) 4y
7. 9x 4(2x 1)
8. (z 2) 2(1 z)
Properties of Real Numbers