Question

The side length, s, of a cube is 3x + 2y. If V = s3, what is the volume of the cube? 3x3 + 18x2y + 36xy2 + 8y3 27x3 + 54x2y + 18xy2 + 2y3 27x3 + 18x2y + 12xy2 + 2y3 27x3 + 54x2y + 36xy2 + 8y3

Answer 1

We are given side length of a cube = (3x+2y).

Volume is given by formula $V=s^3$, where s is the side of cube.

We have s = (3x+2y).

Plugging s = (3x+2y) in formula now.

We get,

$V=(3x+2y)^3$

Expanding by applying formula $(a+b)^3=(a)^3 + 3a^2b+3b^2a+(b)^3.$

$(3x+2y)^3 =(3x)^3+3(3x)^2(2y)+3(2y)^2(3x)+(2y)^3$

$(3x+2y)^3 = 27x^3+54x^2y+36xy^2+8y^3$

Therefore, correct option is 4th option : $27x^3 + 54x^2y + 36xy^2 + 8y^3$.