Question

A student forms a box from a 10 in. by 15 in. piece of cardboard by cutting a square with side length x out of each corner and folding up the sides. How do you write and simplify an expression for the area of the base of the box?

Answer 1

`4x^2-50x+150`

Explanation:

The base of the box is the rectangle made up of the dashed lines in the image.
Thus the length of the base is `15-2x` and the width of the box is `10-2x`

The area of the base is length*width`=(15-2x)(10-2x)`

Multiplying out gives
`150-50x+4x^2`

In standard form this is `4x^2-50x+150`