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.