+537 What is the coefficient of \(x^2y^6\) in the expansion of \(\left(\frac{3}{5}x-\frac{y}{2}\right)^8\) ? Express your answer as a common fraction.
expand (3/5 x - y/2)^8
(6561 x^8)/390625 - (8748 x^7 y)/78125 + (5103 x^6 y^2)/15625 - (1701 x^5 y^3)/3125 + (567 x^4 y^4)/1000 - (189 x^3 y^5)/500 + (63 x^2 y^6)/400 - (3 x y^7)/80 + y^8/256 (9 terms).
It is the 7th term =8 nCr 6 * (3/5 x)^(8 - 7 + 1) * (-y/2)^(7 - 1)
Or: 63/400x^2y^6
