5
advanced-math

Which expression is equivalent to (2x5)2(2x - 5)^2?

A

4x2254x^2 - 25

B

4x2+254x^2 + 25

C

4x210x+254x^2 - 10x + 25

D

4x220x+254x^2 - 20x + 25

Correct Answer: D

Choice D is the correct answer. To expand a binomial squared (ab)2(a - b)^2, use the formula a22ab+b2a^2 - 2ab + b^2.

  1. Here a=2xa = 2x and b=5b = 5.
  2. a2=(2x)2=4x2a^2 = (2x)^2 = 4x^2.
  3. 2ab=2(2x)(5)=20x-2ab = -2(2x)(5) = -20x.
  4. b2=52=25b^2 = 5^2 = 25.

Combine them: 4x220x+254x^2 - 20x + 25.

Choice A is incorrect because it misses the middle term. This is a very common mistake. Choice B is incorrect because it also misses the middle term. Choice C is incorrect because the middle term is calculated as 2(x)(5)-2(x)(5) instead of 2(2x)(5)-2(2x)(5).