# binomial expansion

• April 10th 2010, 06:27 AM
shawli
binomial expansion
Find the coefficient of $\frac{1}{x^3}$ in the expansion of $(x-1)^3 (\frac{1}{x}+x)^6$.
• April 10th 2010, 06:53 AM
sa-ri-ga-ma
Quote:

Originally Posted by shawli
Find the coefficient of $\frac{1}{x^3}$ in the expansion of $(x-1)^3 (\frac{1}{x}+x)^6$.

Expansion of (x - 1)^3 = x^3 - 3x^2 + 3x - 1
First two terms of (1/x + x )^6 = 1/x^6 + 6/x^4 + ...........
So 1/x^3 term will be available by the product of x^3*1/x^6 and 3x*6/x^4
So the coefficient of 1/x^3 = ........?