Question

The McDonald's Play Place is going to increase its ball pit size to allow for more fun! The ball pit was originally 10 feet by 12 feet. They have decided to increase each side by the same amount. Express the area of the new pit as a polynomial in simplest form.

Answer 1

A = x² + 22x + 120

Explanation:

Since the ball pit was originally 10 feet by 12 feet and each side is increased by the same amount which we would call x, the new length of sides are thus 10 + x and 12 + x respectively.

The area of the new pit is thus A = (10 + x)(12 + x), since it is a rectangle.

Expanding the brackets, we have

A = 10 × 12 + 10x + 12x + x²

collecting like terms, we have

A = 120 + 22x + x²

A = x² + 22x + 120