6
advanced-math

Which expression is equivalent to x210x+25x^2 - 10x + 25?

A

(x5)2(x - 5)^2

B

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

C

(x5)(x+5)(x - 5)(x + 5)

D

(x10)2(x - 10)^2

Correct Answer: A

Choice A is the correct answer.

  1. Check first term: x2x^2.
  2. Check last term: 25=(5)225 = (-5)^2.
  3. Check middle term: 2(x)(5)=10x2(x)(-5) = -10x.

This is a perfect square trinomial matching (ab)2(a-b)^2. Thus, (x5)2(x - 5)^2.

Choice B is incorrect because the middle term would be positive. Choice C is incorrect because this is a difference of squares (x225x^2 - 25). Choice D is incorrect because the constant would be 100.