## Algebra 1: Common Core (15th Edition)

Published by Prentice Hall

# Chapter 1 - Foundations for Algebra - 1-7 The Distributive Property - Lesson Check - Page 49: 5

Not like terms.

#### Work Step by Step

This problem deals with combining like terms. 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 $15x^0$ because $x^0$ is equal to 1. In the example, x and y are not both raised to the same power in both expressions, so these are not like terms.

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