A-maths!!!!!!!!!

(1 - 4x + 4x^2)^5
= [ 1 + 4x(x - 1) ]^5
= 1 + (5C1)4x(x - 1) + (5C2)16x^2(x - 1)^2 + (5C3)64x^3(x - 1)^3 + ...
= 1 + 20x^2 - 20x + 160x^2(x^2 - 2x + 1) + 640x^3(x^3 + ... - 1) + ...
= 1 + 20x^2 - 20x - 320x^3 + 160x^2 - 640x^3 + ...
= 1 - 20x + 180x^2 - 960x^3 + ...

豬油包's answer above is correct. However, it should be more nicely presented.
E.g.(1) Write everything in ascending power (don't write "(x - 1)" which is descending power!) as the question suggests the final answer to be.
E.g.(2) Add brackets to separate the many terms into groups.

(1 - 4x + 4x^2)^5
= [ 1 + 4x(x - 1) ]^5
= 1 + (5C1)4x(x - 1) + (5C2)16x^2(x - 1)^2 + (5C3)64x^3(x - 1)^3 + ...
= 1 + 20x^2 - 20x + 160x^2(x^2 - 2x + 1) + 640x^3(x^3 + ... - 1) + ...
= 1 + 20x^2 - 20x - 320x^3 + 160x^2 - 640x^3 + ...
= 1 - 20x + 180x^2 - 960x^3 + ...

(1-4x+4x^2)^5
=[1-x(4-4x)]^5
=(5C0)(1)^5-(5C1)[x(4-4x)]+(5C2)[x(4-4x)]^2-(5C3)[x(4-4x)]^3.................
=1-20x+20x^2+10x^2(16-32x+16x^2)-10x^3(64+....)+.......
=1-20x+20x^2+160x^2-32x^3-640x^3+....
=1-20x+180x^2-682x^3+........