Advanced Math practice question

Answer: A. (x − 3)(x + 3)

x² − 9 is a difference of two squares, x² − 3². A difference of squares a² − b² always factors as (a − b)(a + b), so this is (x − 3)(x + 3). Check: the middle terms 3x and −3x cancel, leaving x² − 9.

Why the other answers are wrong

B. (x − 3)²

(x − 3)² expands to x² − 6x + 9 — a plus 9 and an extra −6x. Squaring a binomial never produces a plain difference of squares.

C. (x − 9)(x + 1)

(x − 9)(x + 1) expands to x² − 8x − 9. The constant is right by coincidence, but there's a −8x term that x² − 9 doesn't have.

D. (x + 3)²

(x + 3)² expands to x² + 6x + 9. Both the sign of the constant and the presence of a middle term are wrong.

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