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Learning Targets

• Given an expression, I can use various strategies to write an equivalent expression.
• When I look at an expression, I can notice if some parts have common factors and make the expression shorter by combining those parts.

Combining like terms is a useful strategy that we will see again and again in our future work with mathematical expressions. It is helpful to review the things we have learned about this important concept.

• Combining like terms is an application of the distributive property. For example:

2x + 9x

(2 + 9) • x

11x

• It often also involves the commutative and associative properties to change the order or grouping of addition. For example:

2a + 3b + 4a + 5b

2a + 4a + 3b + 5b

(2a + 4a) + (3b + 5b)

6a + 8b

• We can't change order or grouping when subtracting; so in order to apply the commutative or associative properties to expressions with subtraction, we need to rewrite subtraction as addition. For example:

2a - 3b - 4a - 5b

2a + -3b + -4a + -5b

(2a + -4a) + (-3b + -5b)

-2a + -8b

-2a - 8b

• Since combining like terms uses properties of operations, it results in expressions that are equivalent.
• The like terms that are combined do not have to be a single number or variable; they may be longer expressions as well. Terms can be combined in any sum where there is a common factor in all the terms. For example, each term in the expression 5(x + 3) - 0.5(x + 3) + 2(x + 3) has a factor of (x + 3). We can rewrite the expression with fewer terms by using the distributive property:

5(x + 3) - 0.5(x + 3) + 2(x + 3)

(5 - 0.5 + 2)(x + 3)

6.5 (x + 3)

Match each expression in column A with an equivalent expression from column B.

Write each expression with fewer terms. Show or explain your reasoning.

1. 3 • 15 + 4 • 15 - 5 • 15
2. 3x + 4x - 5x
3. 3(x - 2) + 4(x - 2) - 5(x - 2)

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