Chapter ISG, Problem 8.3.5P

To determine

To find and simplify an expression

Answer to Problem 8.3.5P

Volume of the rectangular prism is $8x^3+28x^2-16x$ .

Explanation of Solution

Given information:

Length of prism= $x+4$

Breadth of prism= $2x-1$

Height of prism= $4x$

Formula used:

Volume of cuboid=( $length\times breadth\times height$ )

Calculation:

Substituting values,

Volume= $(x+4)(2x-1)(4x)$

Multiplying,

Volume= $\{x(2x-1)+4(2x-1)\}(4x)$

Now,

Volume= $\{2x^2-x+8x-4\}(4x)$

Multiplying again,

Volume= $8x^3-4x^2+32x^2-16x$

Subtracting terms,

Volume= $8x^3+28x^2-16x$

Hence, volume of the rectangular prism is $8x^3+28x^2-16x$ .