College Algebra (6th Edition)

Published by Pearson
ISBN 10: 0-32178-228-3
ISBN 13: 978-0-32178-228-1

Chapter P - Prerequisites: Fundamental Concepts of Algebra - Exercise Set P.5 - Page 75: 121

Answer

Factor of formula = (a - b)(a + b)(4a)

Work Step by Step

Given rectangular solids are rectangular prisms Volume of larger rectangular solid = (Area of larger rectangular solid base $\times$ height of rectangular solid) Base of rectangular solid is a square so the area of larger rectangular base = $a^{2}$ (given that the side of squre is a) Height of rectangular solid = 4a Volume of larger rectangular solid = $a^{2}$ $\times$ 4a Volume of smaller rectangular solid = (Area of smaller rectangular base $\times$ height of rectangular solid) Base of rectangular solid is a square so the area of smaller rectangular base = $b^{2}$ (given that the side of squre is b) Height of rectangular solid = 4a Volume of larger rectangular solid = $b^{2}$ $\times$ 4a Volume of the region outside smaller rectangular solid and inside larger rectangular solid = Volume of larger rectangular solid - Volume of smaller rectangular solid Volume of the region outside smaller rectangular solid and inside larger rectangular solid = ($a^{2}$ $\times$ 4a) - ($b^{2}$ $\times$ 4a) = ($a^{2}$ - $b^{2}$) $\times$ 4a Formula for the Volume of the region outside smaller rectangular solid and inside larger rectangular solid = ($a^{2}$ - $b^{2}$) 4a Use the formula ($a^{2}$ - $b^{2}$) =(a-b)(a+b) Factor of formula =(a-b)(a+b)(4a)
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