A rectangular garden is four times as long as it is wide. Let w represent the width of the garden. Write two equivalent expressions that represent the area of the garden. Justify your answer.

Let's first determine the length. If w is the width of the garden, and the length is 4 times the width, then l=4w. Now, let's think of the area of a rectangle. Area equals length times width (l*w) in a rectangle. So, since l=4w, we can substitute 4w in for l: 4w*w. That's one expression. Now, let's make an equivalent expression. 4w is really 4*w, so we have 4*w*w. w*w=w squared, so another equivalent expression is 4w^2. (Note that ^2 means "squared.")

Answer: 4w*w, 4w^2