Perimeter as a Polynomial

A polynomial can describe a quantity that depends on an unknown. Suppose a rectangle has width w, and its length is 3 units longer, so the length is w + 3. The perimeter is the distance around the rectangle: two lengths plus two widths.

The rectangle has two sides of length w + 3 and two sides of length w. So its perimeter is p = 2(w + 3) + 2w. This formula works for every value of w.

Expand 2(w + 3) + 2w to get 2w + 6 + 2w. Combine the w terms to get p = 4w + 6. The two formulas give the same perimeter. The first one shows where each side comes from, and the second one is shorter to use.