Math Equation about rugs

Question

A rectangular rug is placed on a rectangular floor. The width of the floor is 4 feet greater than the length, X, of the four. The width of the rug is 2 feet less than the width of the floor. The length of the rug is 4 feet less than the width of the rug. what function , R(x), represents the area of the floor not covered by the rug?

Answer 1

the length of floor = x, then the width of floor = x + 4

the area of floor = x(x+4) = x² + 4x;

the width of rug = (x+4) - 2 = x+2, the length of rug = (x+2) - 4 = x-2

the area of rug = (x+2)(x-2) = x²- 4

Therefore, the R(x) = the area of floor - area of rug = (x² + 4x) - (x²- 4) = 4x + 4