Pascal's triangle, 4th row:
1
1 1
1 2 1
1 3 3 1
If we had (a + b)^3, the answer would be a^3 + 3a^2b + ab^2 + b^3, but in this problem we have a = 2x and b = -1, so we get:
(2x)^3 + 3(2x)^2(-1) + 3(2x)(-1)^2 + (-1)^3
8x^3 - 3(4x^2) + 6x - 1
8x^3 - 12x^2 + 6x - 1