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 - Chapter Review - Page 537: 41



Work Step by Step

To find the areas of a rectangle, we use the formula $A=bh$. We plug in the dimensions to get $A=(3x+5)(x+7)$ To use the FOIL method, we multiply the first terms of each binomial, the first term of the first binomial and the last term of the second binomial, the last term of the first binomial and the first term of the second binomial, and the last terms of each binomial. We then find the sum of these products and combine the like terms to get our answer. We apply this method to $(3x+5)(x+7)$:$$(3x+5)(x+7)=3x^2+5x+21x+35=3x^2+26x+35$$This answer is already in standard form because the exponents are in descending order. Therefore, the area of the rectangle is $A=3x^2+26x+35$.
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