Algebra 1

Published by Prentice Hall
ISBN 10: 0133500403
ISBN 13: 978-0-13350-040-0

Chapter 8 - Polynomials and Factoring - 8-2 Multiplying and Factoring - Practice and Problem-Solving Exercises: 28

Answer

$9x^2(4\pi-1)$

Work Step by Step

The area of the yellow part is the total area of the circle reduced by the area taken up by red square. The area of the circle is $\pi r^2=\pi(6x)^2=36\pi x^2$ The total area of the red square is $l\times w=3x\times3x=9x^2$ The area of the yellow part is the total area of the circle reduced by the area taken up by red square. $36\pi x^2-9x^2$ Find the greatest common factor of the terms. Find the prime factors of each term. Multiply the common factors to find the GCF. $36\pi x^2=\underline3\times\underline3\times4\times\pi \times\underline x\times\underline x$ $9x^2=\underline3\times\underline3\times\underline x\times\underline x$ GCF$=3\times3\times x\times x=9x^2$ Factor the GCF out of each term. Use the factors that were not part of the GCF. $36\pi x^2-9x^2=9x^2(4\pi-1)$
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