The sides of a square all have a side length of y. Write a simplified area function in terms of y for a rectangle whose length is twice the side length of the square and whose width is 2 units longer than the side length of the square.
Let's start by finding the side length of the rectangle. Since the length of the rectangle is twice the side length of the square, it will be 2y. And since the width of the rectangle is 2 units longer than the side length of the square, it will be y + 2.
The area of a rectangle is found by multiplying the length by the width. So the area, A, of the rectangle in terms of y will be:
A = (2y)(y + 2)
A = 2y^2 + 4y
Therefore, the simplified area function in terms of y for the given rectangle is 2y^2 + 4y.