Write down and simplify the first four terms in the expansion of [1- (x/2)]^10.
Hence find the coefficient of x^3 in the expansion of (5+4x)(1 - x/2))^10.

My workings:

[1- (x/2)]^10 = 1 + 10C1 (-x/2) + 10C2 (-x/2)^2 + 10C3 (-x/2)^3 + ...
= 1 + 10 (-x/2) + 45 (x^2/4) + 120 (-x^3/8) + ...
= 1 - 5x + 45x^2/4 + 15x^3 + ...


(5+4x)(1-x/2)^10 = (5+4x)(1-5x+45x^2/4 + 15x^3)
= (5*15)x^3 + (4*45/x)x^3
= 75x^3 + 180x^3/4
= 75x^3 + 45x^3

coefficient of x^3 = 75+45 = 120

The answer is -30...Please help me check my workings and correct me...It would be best for you to show your workings step-by-step..Thanks.


Also, can help me do this question?:

[x-(2/x^2)]^16

Thanks.