Algebra 1: Common Core (15th Edition)

Published by Prentice Hall
ISBN 10: 0133281140
ISBN 13: 978-0-13328-114-9

Chapter 1 - Foundations for Algebra - 1-7 The Distributive Property - Practice and Problem-Solving Exercises - Page 50: 64



Work Step by Step

Like terms are terms that have the same variable raised to the same power. Note, by this definition, numbers like 10 and 15 are also like terms as they are multiplied by a variable raised to the zeroth power. This concept may seem confusing, but it makes sense if we consider it for a second. Anything raised to the zeroth power is one. Thus, $x^{0}$ is 1. Earlier in the chapter, we learned the Identity Property of Multiplication, which states that anything times one is itself. Thus, 15 is equal to 15$x^{0}$ because $x^{0}$ is equal to 1. Now, back to the problem. Recall, if terms are like terms, we can add or subtract these terms just like we add or subtract numbers. Thus, because 10ab and 9ab are the only like terms, we can subtract them to simplify the expression to $ 2a$$b^{2}$$+ab$
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