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# Combining Like Terms Practice Questions

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Updated on Sep 23, 2011

## Introduction

In these practice questions, you will practice simplifying algebraic expressions. As you do this, you will recognize and combine terms with variables that are alike and link them to other terms using the arithmetic operations.

You should know that

• the numbers in front of the variable or variables are called coefficients.
• a coefficient is just a factor in an algebraic term, as are the variable or variables in the term.
• like terms can have different coefficients, but the configuration of the variables must be the same for the terms to be alike. For example, 3x and –4x are like terms but are different from 7ax or 2x3.

You can think of an algebraic term as a series of factors with numbers, and you can think of variables as factors. When the variables are given number values, you can multiply the factors of a term together to find its value, as you did in Chapter 2. When you have terms that are alike, you can add or subtract them as if they were signed numbers. You may find that combining like terms may be easier if you do addition by changing all subtraction to addition of the following term with its sign changed. This strategy will continue to be shown in the answer explanations. But as you either know or are beginning to see, sometimes it's easier to just subtract.

You will also use the important commutative and associative properties of addition and multiplication. Another important and useful property is the distributive property. See the Tips for Combining Like Terms.

## Tips for Combining Like Terms

### Distributive Property of Multiplication

The distributive property of multiplication tells you how to multiply the terms inside a parentheses by the term outside the parentheses. Study the following general and specific examples.

a(b + c) = ab + ac
a(bc) = abac
(b + c)a = ba + ca
4(6 + 3) = 4 · 6 + 4 · 3 = 24 + 12 = 36
(–5 + 8)3 = –5 · 3 + 8 · 3 = –15 + 24 = 9
7(10 + 3) = 7 · 10 + 7 · 3 = 70 + 21 = 91
3(x + 2y) = 3 · x + 3 · 2y = 3x + 6y
a(b – 5d) = a · ba · 5d = ab – 5ad

Numerical examples of the commutative properties for addition and multiplication were given in the Tips for Working with Integers. Now look at the following examples:

### Commutative Property of Addition

a + b = b + a

This equation reminds us that terms being combined by addition can change their location (commute), but the value of the expression remains the same.

### Commutative Property of Multiplication

x · y = y · x

This equation reminds us that the order in which we multiply expressions can change without changing the value of the result.

### Associative Property of Addition

(q + r) + s = q + (r + s)

This equation reminds us that when you are performing a series of additions of terms, you can associate any term with any other and the result will be the same.

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