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?

8x3+36x2+54x+27
8 x cubed plus 36 x squared plus 54 x plus 27

8x3−36x2+54x+27
8 x cubed minus 36 x squared plus 54 x plus 27

8x3+36x2+54x−27
8 x cubed plus 36 x squared plus 54 x minus 27

8x3−36x2+54x−27

1 answer

The correct expression for the new volume of the cube is:

8x^3 - 36x^2 + 54x - 27

This is because when the side length of 2x is reduced by 3 units, the new side length becomes 2x - 3. The volume of a cube is given by (side length)^3, so the new volume can be expressed as (2x - 3)^3. Applying the Binomial Theorem to expand this expression, we get:

(2x - 3)^3 = 8x^3 - 36x^2 + 54x - 27