Intermediate Algebra (6th Edition)

Published by Pearson
ISBN 10: 0321785045
ISBN 13: 978-0-32178-504-6

Chapter 1 - Section 1.4 - Properties of Real Numbers and Algebraic Expressions - Exercise Set - Page 39: 49



Work Step by Step

To find a product using the distributive property, you take the coefficient and multiply it by each term within the parentheses separately. The negative sign represents a coefficient of $-1$. The first term within the parentheses is $2a$, so the first term of the product is $-1\times2a$, or $-2a$. The second term within the parentheses is $b$, so the second term of the product is $-1\times b$, or $-b$. The terms within the parentheses are connected by a plus sign, so the terms within the product will be too. However, since the term you are adding is negative, and adding a negative is in this case about the same as subtracting a positive, the product can be expressed as a difference (using a minus sign). The final product, therefore, is $-2a+(-b)$, or $-2a-b$.
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