Thinking Mathematically (6th Edition)

Published by Pearson
ISBN 10: 0321867327
ISBN 13: 978-0-32186-732-2

Chapter 6 - Algebra: Equations and Inequalities - 6.1 Algebraic Expressions and Formulas - Exercise Set 6.1: 83

Answer

The statement makes sense.

Work Step by Step

The expression, as written, makes sense because the second term can be rewritten using the Commutative Property of Multiplication. The Commutative Property of Multiplication states that when we multiply two or more numbers/terms together, the order in which we multiply will not affect our final answer. Note: This only works if multiplication is the only operation are doing. Using the commutative property of multiplication, we can take the original writing of the expression and rewrite is as noted below. The only change made was reordering the multiplication in the second term. 2$x^{2}$y - 2y$x^{2}$ may be rewritten as 2$x^{2}$y - 2$x^{2}$y. When we rewrite the expression, it gives shows us that the two terms are exactly alike. So, when we subtract a term or number from itself, we will always get zero.
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