Maths

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

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asked by Emma
  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

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    posted by Reiny

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