Question

Factoring! (y-1)^3 + 27x^3 The answer is (y+3x-1)(y^2 - 2y-3xy+9x^2 +3x+1), but I don't understand how to get there. I know that you use the substitution method and it's the sum of a cube.

Answer 1

yes it is the sum of two cubes

Answer 2

\[(a+b)(a^2-ab+b^2)\] with
\[a=(y-1), b =3x\] you get
\[((y-1_+3x)((y-1)^2-(y-1)3x+(3x)^2)\]

Answer 3

this gives
\[(y+3x-1)(y^2-2y+1-3xy+3x+9x^2)\] and finally to your answer