Answer
$$(v+w)\cdot v-(v+w)\cdot w = \|v\|^2-\|w\|^2.$$
Work Step by Step
Using the properties of the dot product, we have
$$(v+w)\cdot v-(v+w)\cdot w\\
=v\cdot v +v\cdot w-v\cdot w-w\cdot w\\
=v\cdot v-w\cdot w= \|v\|^2-\|w\|^2.$$
Calculus (3rd Edition)
by Rogawski, Jon; Adams, Colin
Published by
W. H. Freeman
ISBN 10:
1464125260
ISBN 13:
978-1-46412-526-3
Chapter 13 - Vector Geometry - 13.3 Dot Product and the Angle Between Two Vectors - Exercises - Page 666: 37
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