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: 30

Answer

$\dfrac{1}{7}x^{2}-\dfrac{1}{3}x+\dfrac{2}{3}$

Work Step by Step

$\Big(\dfrac{1}{3}x^{2}-\dfrac{2}{7}x\Big)-\Big(\dfrac{4}{21}x^{2}+\dfrac{1}{21}x-\dfrac{2}{3}\Big)$ Remove both parentheses. To remove the second one, change the sign of every term inside it: $\dfrac{1}{3}x^{2}-\dfrac{2}{7}x-\dfrac{4}{21}x^{2}-\dfrac{1}{21}x+\dfrac{2}{3}=...$ Simplify by combining like terms: $...=\Big(\dfrac{1}{3}-\dfrac{4}{21}\Big)x^{2}-\Big(\dfrac{2}{7}+\dfrac{1}{21}\Big)x+\dfrac{2}{3}=...$ $...=\dfrac{21-12}{63}x^{2}-\dfrac{42+7}{147}x+\dfrac{2}{3}=\dfrac{9}{63}x^{2}-\dfrac{49}{147}x+\dfrac{2}{3}=...$ $...=\dfrac{1}{7}x^{2}-\dfrac{1}{3}x+\dfrac{2}{3}$
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