Intermediate Algebra (6th Edition)

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

Chapter 5 - Section 5.4 - Multiplying Polynomials - Exercise Set: 107

Answer

The area of the shaded region is $8x^2-12x+4$ square inches.

Work Step by Step

RECALL: The area of a square is given by the formula $A=s^2$ where s = side length. The figure involves two squares. The area of the shaded region is equal to the area of the bigger square minus the area of the smaller square. Thus, the area of the shaded region in square inches is: $\\=\text{area of the bigger square} - \text{area of the smaller square} \\=(3x-2)^2-x^2 \\=[(3x)^2-2(3x)(2)+2^2]-x^2 \\=9x^2-12x+4-x^2 \\=8x^2-12x+4$
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