Elementary Geometry for College Students (7th Edition) Clone

Published by Cengage
ISBN 10: 978-1-337-61408-5
ISBN 13: 978-1-33761-408-5

Chapter 8 - Section 8.1 - Area and Initial Postulates - Exercises - Page 361: 46

Answer

$(a+b)^{2}$ = $a^{2}$ + $b^{2}$ + 2ab

Work Step by Step

We know area of square A = side * side The given drawing consist of 4 rectangles The area of Square = (a+b)(a+b)= $(a+b)^{2}$ Lets find the area of all the 4 rectangles separately Rectangle I = ab Rectange II = $b^{2}$ Rectangle III = ab Rectangle IV = $a^{2}$ The total area of square = Area of I + Area of II + Area of III + Area of IV = ab+ $b^{2}$+ab+ $a^{2}$ =2ab+ $b^{2}$ + $a^{2}$ Therefore $(a+b)^{2}$ = $a^{2}$ + $b^{2}$ + 2ab
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