The figure above represents a rectangular portrait within a frame 3 inches wide. The expression 3x2−(3x−6)(x−6) represents the area of the frame, in square inches. What does the
quantity (3x−6)(x−6) represent?
Approach
It might be easier to identify what 3x2 refers to. It is the area of the larger rectange, or the combined area of the frame and portrait.
3x2−(3x−6)(x−6)Area=l⋅wArea=3x⋅x=3x2
To find the area of the frame only, we must subtract the area of the inner rectange (portrait). From our equation, the remaining part must then be the area of the inner rectangle.
area of frame and portrait3x2−area of portrait(3x−6)(x−6)