# 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?

May 31, 2016

$4 {x}^{2} - 50 x + 150$

#### 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 $15 - 2 x$ and the width of the box is $10 - 2 x$

The area of the base is length*width$= \left(15 - 2 x\right) \left(10 - 2 x\right)$

Multiplying out gives
$150 - 50 x + 4 {x}^{2}$

In standard form this is $4 {x}^{2} - 50 x + 150$