Advanced Math practice question

Answer: A. (2x − 5)(2x + 5)

4x² is (2x)² and 25 is 5², so this is a difference of squares: (2x)² − 5² = (2x − 5)(2x + 5). Check: the middle terms 10x − 10x cancel.

Why the other answers are wrong

B. (4x − 5)(x + 5)

(4x − 5)(x + 5) expands to 4x² + 15x − 25 — there's a stray 15x. The two factors must be the same except for the sign in the middle.

C. (2x − 5)²

(2x − 5)² expands to 4x² − 20x + 25: a plus 25 and a middle term. A perfect square never gives a plain difference.

D. (4x − 25)(x + 1)

(4x − 25)(x + 1) expands to 4x² − 21x − 25. The middle term shouldn't be there.

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