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11) Using the binomial theorem to find the coefficient of the x^4y^13 term in (3x-y)^17

11) Using the binomial theorem to find the coefficient of the x^4y^13 term in (3x-example-1
User BlackXero
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1 Answer

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The binomial theorem states that:


(x+y)^n=\sum ^n_(k\mathop=0)(n!)/(k!(n-k)!)x^(n-k)y^k

In this case we have the polynomial


(3x-y)^(17)

to get the term:


x^4y^(13)

we need k=13, this means that this term will be given as:


\begin{gathered} (17!)/(13!(17-13)!)(3x)^(17-13)(-y)^(13)=2380(3x)^4(-y)^(13) \\ =2380(81x^4)(-y^(13))^{} \\ =-192780x^4y^(13) \end{gathered}

Therefore we conclude that the coefficient of the term is -192780

User Anjisan
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