Functions Modeling Change: A Preparation for Calculus, 5th Edition

Published by Wiley
ISBN 10: 1118583191
ISBN 13: 978-1-11858-319-7

Chapter 1 - Linear Functions and Change - 1.2 Rate of Change - Exercises and Problems for Section 1.2 - Skill Refresher: S8

Answer

$$3x^{2}+2xb−b^{2}$$

Work Step by Step

Initially: $4x^{2}−(x-b)^{2}$ First, rewrite the $(x-b)^{2}$ in its expanded form: $(x-b)(x-b)$ Then FOIL it: $$4x^{2}−(x^{2}-2xb+b^{2})$$ After that, distribute the negative: $$4x^{2}−x^{2}+2xb−b^{2}$$ Then simplify by combining like terms: $$3x^{2}+2xb−b^{2}$$
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