Question

Philip and Laura want to build a pool in their backyard. The length and width of the pool can be represented by the equation f(x) = (x-3) (5x + 2) feet. What is the area of Philip and Laura's pool? You must show your work, and include your units of measurement.​

Answer 1

The length and width of the pool are given by the expression f(x) = (x-3) (5x + 2) feet. To find the area of the pool, we need to multiply the length and width together:

Area = length x width

Area = f(x) x f(x)

Area = (x-3) (5x + 2) x (x-3) (5x + 2)

Area = (x-3)^2 (5x + 2)^2

Expanding this expression, we get:

Area = (25x^2 - 6x - 6)^2 square feet

Therefore, the area of Philip and Laura's pool is (25x^2 - 6x - 6)^2 square feet. Note that we cannot determine a numerical value for the area without knowing the value of x.