Question

How do you factor: #y= x^3 - 27 #?

Answer 1

`y=x^3-27=(x-3)(x^2+3x+9)`

Explanation:

Both `x^3` and `27=3^3` are perfect cubes. So it is natural to use the difference of cubes identity:

`a^3-b^3=(a-b)(a^2+ab+b^2)`

with `a=x` and `b=3` as follows:

`x^3-27`

`=x^3-3^3`

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

`=(x-3)(x^2+3x+9)`