The side length, s, of a cube is x - 2y. If V = s³, what is the volume of the cube?

Solution:

Given the length of the side s = x - 2y

If the length of the cube is s units, the volume of the cube is given by s³ cubic units.

The volume of the cube V = s³

Substituting the value of s in the above formula we get

V = (x - 2y)³

Using the cube of the binomial formula, (a-b)³ = a³ -3a²b+3ab²+b³

(x - 2y)³ = x³ - 6x²y +6xy² - 8y³

The side length, s, of a cube is x - 2y. If V = s³, what is the volume of the cube?

Summary:

The volume of the cube V = x³ - 8y - 6x²y +6xy² - 8y³