A picture is mounted on a square mat. The mat has a side length of (2x + 3) inches. The picture itself is a square with side length (2x − 1) inches, centered on the mat. Which polynomial represents the area of the mat that is NOT covered by the picture?
A8x + 8
B12x + 8
C16x + 10
D16x + 8
Explanation
Mat area: (2x + 3)² = 4x² + 12x + 9. Picture area: (2x − 1)² = 4x² − 4x + 1. Uncovered = mat − picture = (4x² + 12x + 9) − (4x² − 4x + 1) = (12x − (−4x)) + (9 − 1) = 16x + 8 sq in. Choice A drops the 4x² cancellation but only takes half the linear coefficient. B forgets to flip the sign of −4x when subtracting. C carries an off-by-one constant.
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