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

a) x3 - 6x2y + 12xy2 - 8y3

b) x3 + 6x2y + 12xy2 + 8y3

c) 3x3 - 6x2y + 12xy2 - 24y3

d) 3x3 + 6x2y + 12xy2 + 24y3

The answer is a) x3 - 6x2y + 12xy2 - 8y3

To calculate this, we will use the following algebra expansion:

(a - b) ³ = a³ - 3a²b + 3ab² - b³

In our example, a is x while b is 2y.

If:

s = x - 2y

Then:

V = s³ = (x - 2y) ³

V = x³ - 3 · x² · 2y + 3 · x · (2y) ² - (2y) ³

V = x³ - 3 ·2 ·x²y + 3 · x · 2² · y² - 2³ · y³

V = x³ - 6x²y + 3 · x · 4 · y² - 8 · y³

V = x³ - 6x²y + 3 · 4 · xy² - 8y³

V = x³ - 6x²y + 12xy² - 8y³