The figure above represents a rectangular portrait within a frame 3 inches wide. The expression \(3x^2-(3x-6)(x-6)\) represents the area of the frame, in square inches. What does the quantity \((3x-6)(x-6) \) represent?

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It might be easier to identify what \(3x^2\) refers to. It is the area of the larger rectange, or the combined area of the frame and portrait.

$$ 3x^2-(3x-6)(x-6)$$ $$ \text{Area}=l\cdot w $$ $$ \text{Area}=3x \cdot x $$ $$ = 3x^2 $$

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.

$$ \underbrace{3x^2}_\text{area of frame and portrait}-\underbrace{(3x-6)(x-6)}_\text{area of portrait}$$