## Precalculus (6th Edition) Blitzer

$V=3a(a+b)(a-b)$
The larger rectangular prism has volume=(base area)$\times$height, $V_{1}=a^{2}(3a)=4a^{3}$ The inner rectangular prism has volume $V_{2}=b^{2}(3a)=3ab^{2}$ The volume we are after is $V=V_{1}-V_{2}=3a^{3}-3ab^{2}$ $=3a(a^{2}-b^{2})\qquad$... a difference of squares, $V=3a(a+b)(a-b)$