Question

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

Answer 1

`x^3 -6x^2y + 12xy^2 - 8y^3`

Explanation:

We are given that the side length (s) of a cube is
`x-2y`. Given that
`V=s^3`, we are to find the volume of the cube.

`Volume =  (x-2y)^3`

We know that,
`(a - b)^3 = a^3 - 3a^2b + 3ab^2 - b^3`

So expanding the given expression accordingly:

`(x-2y)^3 = x^3 - (3 * x^2 * 2y) + (3 * x * (2y)^2) - (2y)^3`

Volume of cube =
`x^3 -6x^2y + 12xy^2 - 8y^3`

Answer 2

The volume of cube = x³ -6x²y + 12xy² - 8y³

Explanation:

It is given that,

Side length of cube s = (x - 2y)

Volume of cube = s³

Points to remember

(a - b)³ = a³ - 3a²b + 3ab² - b³

To find the volume of cube

s = (x - 2y)

Volume V = s³ = (x - 2y)³

(x - 2y)³ = x³ - (3 * x² * 2y) + (3 * x * (2y)²) - (2y)³

= x³ -6x²y + 12xy² - 8y³

Therefore the volume of cube = x³ -6x²y + 12xy² - 8y³