The area of a rectangle is expressed as x4 - 9y2. What are the possible dimensions of the rectangle?

This is a stupid question. The teacher who asked this needs to go back to school.

A = x⁴ - 9y²

That's going to be a number. As long as it's positive we can choose any length for our rectangle L and we can compute the width by W=A/L. So the correct answer is the dimensions are L by (x⁴ - 9y²) / L.

They don't want the correct answer. They want you to factor this expression. We'll do it, but don't believe for a second this factoring somehow constrains the possible dimensions of some rectangle.

We use the difference of two squares, a²-b² = (a+b) (a-b)

A = x⁴ - 9y² = (x²) ² - (3y) ² = (x²+3y) (x²-3y)

Answer: x²+3y by x²-3y