Algebra: A Combined Approach (4th Edition)

Published by Pearson
ISBN 10: 0321726391
ISBN 13: 978-0-32172-639-1

Chapter 5 - Section 5.4 - Adding and Subtracting Polynomials - Exercise Set: 29

Answer

$\dfrac{2}{5}z^{2}-\dfrac{3}{10}z+\dfrac{7}{20}$

Work Step by Step

$\Big(\dfrac{1}{4}z^{2}-\dfrac{1}{5}z\Big)-\Big(-\dfrac{3}{20}z^{2}+\dfrac{1}{10}z-\dfrac{7}{20}\Big)$ Remove both parentheses. To remove the second one, change the sign of every term inside it: $\dfrac{1}{4}z^{2}-\dfrac{1}{5}z+\dfrac{3}{20}z^{2}-\dfrac{1}{10}z+\dfrac{7}{20}=...$ Simplify by combining like terms: $...=\Big(\dfrac{1}{4}+\dfrac{3}{20}\Big)z^{2}-\Big(\dfrac{1}{5}+\dfrac{1}{10}\Big)z+\dfrac{7}{20}=...$ $...=\dfrac{20+12}{80}z^{2}-\dfrac{10+5}{50}z+\dfrac{7}{20}=...$ $...=\dfrac{32}{80}z^{2}-\dfrac{15}{50}z+\dfrac{7}{20}=\dfrac{2}{5}z^{2}-\dfrac{3}{10}z+\dfrac{7}{20}$
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