Hi, I am stuck with a question about Binomial Expansion using Binomial Theorem, here is the question:

Find, in ascending powers of x, the first 4 terms in the expansion of (1 - 2x - 4x^2)^11

Here is how I work out the question:

[1 - 2x(1 + 2x)]^11

= 1 + (11C1)[-2x(1+2x)] + (11C2)[-2x(1+2x)]^2 + (11C3)[-2x(1+2x)]^3 + .........

= 1 + 11[-2x(1+2x)] + 55[-2x(1+2x)]^2 + 165[-2x(1+2x)]^3 + ............

= 1 - 22x - 44x^2 + 55[(2x)^2 - 2(2x)(4x^2) + (4x^2)^2] + 165(-2x - 4x)^3 + ....

= 1 - 22x - 44x^2 + 220x^2 - 880x^3 +880x^4

+ 165[(-2x)^3 + 3(-2x)^2(-4x^2) + 3(-2x)(-4x^2)^2 + (-4x^2)^2

= 1 - 22x - 44x^2 + 220x^2 - 880x^3 +880x^4

+ 165(-8x^3 + 48x^4 + 96x^5 - 64x^6)

= 1 - 22x + 176x^2 - 880x^3 + 880x^4 - 1320x^3 + ...............

= 1 - 22x + 176x^2 -2200x^3

The bold part is the one that is wrong, I am not sure how I do it wrongly, can anyone guide me? thanks

the solution is 1 - 22x + 176x^2 - 440x^3 + .......