4
advanced-math

Simplify: (2x−3)2−5(2x - 3)^2 - 5

A

4x2−12x+44x^2 - 12x + 4

B

4x2−6x+44x^2 - 6x + 4

C

4x2−12x−144x^2 - 12x - 14

D

2x2−12x+42x^2 - 12x + 4

Correct Answer: A

Choice A is the correct answer.

  1. Expand (2x−3)2(2x - 3)^2: (2x)2−2(2x)(3)+32=4x2−12x+9(2x)^2 - 2(2x)(3) + 3^2 = 4x^2 - 12x + 9.
  2. Subtract 5: (4x2−12x+9)−5(4x^2 - 12x + 9) - 5.
  3. Simplify: 4x2−12x+44x^2 - 12x + 4.

Choice B is incorrect because the middle term is −2(2x)(3)=−12x-2(2x)(3) = -12x, not −6x-6x. Choice C is incorrect because it subtracts 5 from -9 (sign error). Choice D is incorrect because (2x)2=4x2(2x)^2 = 4x^2, not 2x22x^2.

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