Question

Find the coefficient of x^7y^4 in the binomial expansion of (1/4*x -16y)^11

so far i have
11Ck(1/4 x)^11-k (-16y)^k=11Ck*(1/4)^11-k *x^11-k *(-16)^k * y^k

Answer 1

Ok so far

simplify your expression a bit and use proper brackets

= 11Ck (1/4)^(11-k) (-16)^k x^(11-k) y^k

so y^k <----> y^4
thus k = 4

the coefficient comes from
11Ck (1/4)^(11-k) (-16)^k
= 11C4 (1/4)^7 (-16)^4
= 330(1/16384)(65536)
= 1320

confirmation:

https://www.wolframalpha.com/input/?i=expand+(x%2F4+-16y)%5E11