In general the binomial expansion is
[tex] (a+b)^n = {n \choose 0} a^0 b^n + {n \choose 1} a^1 b^{n-1} + {n \choose 2} a^2 b^{n-2} + ... + {n \choose n} a^n b^0[/tex]
So in our case, because we want ascending powers of x we'll write,
[tex](-3x + 1)^{11} = {11 \choose 0} (-3x)^0 1^{11} + {11 \choose 1} (-3x)^{1} 1^{10} + {11 \choose 2} (-3x)^{2} 1^9 + {11 \choose 3 } (-3x)^3 1^8 + ... [/tex]
We need to calculate the binomial coefficients:
[tex]{11 \choose 0} = 1[/tex]
[tex]{11 \choose 1} = 11[/tex]
[tex]{11 \choose 2} = \dfrac{11 \times 10}{2} = 55[/tex]
[tex]{11 \choose 3} = \dfrac{11 \times 10 \times 9}{3 \times 2} = 165[/tex]
[tex](-3x+1)^{11} = 1 (-3x)^0 1^{11} + 11(-3x)^{1} 1^{10} + 55 (-3x)^2 1^{9} + 165 (-3x)^3 1^8 + ... [/tex]
[tex](1-3x)^{11} = 1 -33 x + 495 3x^2 - 4455 x^3+ ... [/tex]
