Question

The length of a rectangle is 16 units more than it's with. The area of the rectangle can be expressed as x^4 - 64.

Answer 1

`Width = x^2 - 8`

Explanation:

Given

`L = 16 + W`

`Area = x^4 - 64`

Required

An expression for the width

We have:

`Area = x^4 - 64`

Express as difference of two squares:

`Area = (x^2 + 8)(x^2 - 8)`

For all acceptable values of x,

`x^2 + 8>x^2 - 8`

So:

`Length = x^2 + 8`

`Width = x^2 - 8`