Question bank / Equivalent expressions

Math · Advanced MathEasy

Which expression is equivalent to x2−25x^2 - 25?

A

(x−5)2(x - 5)^2

B

(x−25)(x+1)(x - 25)(x + 1)

C

(x+5)2(x + 5)^2

D

(x−5)(x+5)(x - 5)(x + 5)

Show answer and explanation

Answer: D

A difference of squares factors as a2−b2=(a−b)(a+b)a^2 - b^2 = (a - b)(a + b). Here x2−25=x2−52=(x−5)(x+5)x^2 - 25 = x^2 - 5^2 = (x - 5)(x + 5).

Choice A expands to x2−10x+25x^2 - 10x + 25, which has a middle term and a positive constant.

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