Binomal Theorem

1. (1+ 1/x) ^2 (2-x)^7
= (1+ 2/x + 1/x^2) [(2^7) + 7C1 (2^6)(-x^1) + 7C2 (2^5)(-x^2) + 7C3 (2^4)(-x^3) + 7C4 (2^3)(-x^4) + 7C5 (2^2)(-x^5) + 7C6 (2^1)(-x^6) + (-x^7)]
= (1+ 2/x + 1/x^2) [128 -448x +672x^2 -560x^3 +280x^4 - 84x^5 +14x^6 -x^7]
= (1+ 2/x + 1/x^2) (128 -448x +672x^2 + .....)
a) the constant term
= (1)(128) + (2/x )(-448x) + (1/x^2)(672x^2)
b) the coefficient
= 128 -896 +672
= -96