Question

How do you factor `y= x^3 + 9x^2 + 27x + 27` ?

Answer 1

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

Explanation:

Notice that `x^3` is a perfect cube and `27 = 3^3` is also a perfect cube.

So try `(x+3)^3` to see if the middle two terms match.

In general `(a+b)^3 = a^3+3a^2b+3ab^2+b^3`, so:

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

`=x^3+9x^2+27x+27`