EDGE Math 8

Products of Two Binomials

Example 2

Find a polynomial that represents the volume of the rectangular solid with the given length, width, and height, as shown in the figure below. Assume that $p$ represents a positive real number.

Solution

Let $V$ be the volume of the box.

V = l w h

\to

Use the formula for the volume of a rectangular solid.

= (2 p + 1) (p + 3) (p + 2)

\to

Substitute the given expressions.

= (2 p^{2} + 7 p + 3) (p + 2)

\to

Apply the FOIL method.

= 2 p^{3} + 7 p^{2} + 3 p + 4 p^{2} + 14 p + 6

\to

Apply the distributive property.

= 2 p^{3} + 11 p^{2} + 17 p + 6

\to

Combine like terms.

Hence, the volume of the box is

V = 2 p^{3} + 11 p^{2} + 17 p + 6 cubic units.