Find the coefficient in front of x6 y3 in the binomial expan

Find the coefficient in front of x^6 y^3 in the binomial expansion of (-x + 2y)^9.

Solution

The coefficient for this term is 672

(-x+2y)*9
=9C0(-x)^0(2y)^9+...9C6(-x)^6 (2y)^3+...

So, 9C6(-1)^6(2^3) is the coefficient as the upper binomial expansion suggests.

So, this term above is equal to 672