Question

A rectangular box has a volume x^3-64 cubic inches. If the height of the box x-4 inches, what is the area of the base of the box, in square inches ?

Answer 1

`\purple{ \bold{ \therefore \: A_(base) = {x}^(2) + 4x + 16}}`

Explanation:

`\because \: V_(box) = A_(base) * height \\ \\ \therefore \: A_(base) = (V_(box))/(height) \\ \\ \therefore \: A_(base) = \frac{ {x}^(3) - 64}{(x - 4)} \\ \\ \therefore \: A_(base) = \frac{ {x}^(3) - {4}^(3) }{(x - 4)} \\ \\ \therefore \: A_(base) = \frac{ \cancel{ ({x} - {4})}( {x}^(2) + 4x + {4}^(2) )}{\cancel{ ({x} - {4})}} \\ \\ \purple{ \bold{ \therefore \: A_(base) = {x}^(2) + 4x + 16}}`