4

Set 2: Quadratic Equations (Advanced)

Explanation

Answer: A

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

A.

(x5)2(x - 5)^2

✓ Correct
B.

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

C.

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

D.

(x10)2(x - 10)^2

Detailed Explanation

Choice A is correct. 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) = -10 x. 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.

Key Steps:

The correct answer is (x5)2(x - 5)^2

Why others are wrong:
B: Choice B is incorrect and may result from a calculation error.
C: Choice C is incorrect and may result from a calculation error.
D: Choice D is incorrect and may result from a calculation error.

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