# Chapter P - Prerequisites: Fundamental Concepts of Algebra - Exercise Set P.4: 93

The volume of the rectangular solid is $4x^3-36x^2+80x$ cubic units.

#### Work Step by Step

The formula for the volume of a rectangular solid is $v=lwh$ (volume equals length times width times height. This solid has the dimensions $8-2x$ by $10-2x$ by $x$. $$v=(8-2x)(10-2x)(x)$$ $$v=[(8\times 10)+(8\times (-2x))+(-2x\times 10)+(-2x\times (-2x))](x)$$ $$v=(80-16x-20x+4x^2)(x)$$ $$v=(80-36x+4x^2)(x)$$ $$v=(80\times x)+(-36x\times x)+(4x^2\times x)$$ $$v=80x-36x^2+4x^3$$ The volume is $80x-36x^2+4x^3$ cubic units.

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