A square tile has side length x + 4 centimetres, and a smaller square tile has side length x − 4 centimetres, where x 4. Which of the following expressions gives, for every such x, how many square centimetres larger the first tile's area is than the second's?

Question

A square tile has side length x + 4 centimetres, and a smaller square tile has side length x − 4 centimetres, where x > 4. Which of the following expressions gives, for every such x, how many square centimetres larger the first tile's area is than the second's?

Accepted Answer

A. 16x. The difference is (x + 4)² − (x − 4)² = (x² + 8x + 16) − (x² − 8x + 16) = 16x. Or use a² − b² = (a − b)(a + b) = (8)(2x) = 16x.

Answer

B. 0 — The two areas are not equal, so their difference is not 0.

Answer

C. 32x — 32x doubles the answer — the middle terms are 8x and −8x, giving 16x, not 32x.

Answer

D. 2x² + 32 — 2x² + 32 is the SUM of the two areas.

Advanced Math practice question

Answer: A. 16x

Why the other answers are wrong

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