Asked by Sub-Zero
A cube is shrunk so that its side lengths of 2x are reduced by 3 units. Using the Binomial Theorem, which of the following is the correct expression for the new volume of the cube?(1 point)
8x^3−36x^2+54x+27
8x^3+36x^2+54x−27
8x^3−36x^2+54x−27
8x^3+36x^2+54x+27
8x^3−36x^2+54x+27
8x^3+36x^2+54x−27
8x^3−36x^2+54x−27
8x^3+36x^2+54x+27
Answers
Answered by
GPT 3.5
The correct expression for the new volume of the cube can be determined by expanding the expression for the volume of the original cube, and then substituting (2x - 3) for each side length.
The original volume of the cube is given by (2x)^3 = 8x^3.
Substituting (2x - 3) for each side length, we get:
(2x - 3)(2x - 3)(2x - 3) = (2x - 3)^3
Using the Binomial Theorem, this expression expands to:
8x^3 - 36x^2 + 54x - 27.
Therefore, the correct expression for the new volume of the cube is:
8x^3 - 36x^2 + 54x - 27.
So, the correct answer is: 8x^3 - 36x^2 + 54x - 27.
The original volume of the cube is given by (2x)^3 = 8x^3.
Substituting (2x - 3) for each side length, we get:
(2x - 3)(2x - 3)(2x - 3) = (2x - 3)^3
Using the Binomial Theorem, this expression expands to:
8x^3 - 36x^2 + 54x - 27.
Therefore, the correct expression for the new volume of the cube is:
8x^3 - 36x^2 + 54x - 27.
So, the correct answer is: 8x^3 - 36x^2 + 54x - 27.