Algebra 1: Common Core (15th Edition)

Published by Prentice Hall
ISBN 10: 0133281140
ISBN 13: 978-0-13328-114-9

Chapter 8 - Polynomials and Factoring - 8-4 Multiplying Soecial Cases - Practice and Problem-Solving Exercises - Page 507: 17


$(10x+15) \ \ \mathrm{u}\mathrm{n}\mathrm{i}\mathrm{t}\mathrm{s}^{2}$.

Work Step by Step

Find the total area of the outer square. $(x+4)^{2}$ ...square the binomial. $=x^{2}+2(x)(4)+4^{2}$ ...simplify. $=x^{2}+8x+16$ Find the area of the inner square. $(x-1)^{2}$ ...square the binomial. $=x^{2}-2(x)(1)+1$ ...simplify. $=x^{2}-2x+1$ Find the area of the figure Area of figure=(Area of outer square) - (Area of inner square) $A=x^{2}+8x+16-(x^{2}-2x+1)$ ...remove parentheses. $=x^{2}+8x+16-x^{2}+2x-1$ like terms. $=x^{2}-x^{2}+8x+2x+16-1$ ...add like terms. $=10x+15$ The area of the figure is $(10x+15) \ \ \mathrm{u}\mathrm{n}\mathrm{i}\mathrm{t}\mathrm{s}^{2}$.
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