Question

school of technology students want to build a deck around a 15 foot by 20 foot pool. the deck has a width of x feet. write an expression to represent the area of the pool with the deck included.

Explanation:

Step1: Determine the length of the pool with deck

The original length of the pool is 20 feet, and the deck adds \( x \) feet on both sides. So the new length is \( 20 + 2x \).

Step2: Determine the width of the pool with deck

The original width of the pool is 15 feet, and the deck adds \( x \) feet on both sides. So the new width is \( 15 + 2x \).

Step3: Calculate the area of the pool with deck

The area of a rectangle is length times width. So the area \( A \) is the product of the new length and new width, which is \( A=(20 + 2x)(15 + 2x) \). We can expand this:
\[

$$\begin{align*} (20 + 2x)(15 + 2x)&=20\times15+20\times2x+2x\times15 + 2x\times2x\\ &=300 + 40x+30x + 4x^{2}\\ &=4x^{2}+70x + 300 \end{align*}$$

\]

Answer:

The expression for the area of the pool with the deck included is \( 4x^{2}+70x + 300 \) (or in factored form \( (20 + 2x)(15 + 2x) \)).