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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 X4y13 Term In 3xy17 class=

Sagot :

The binomial theorem states that:

[tex](x+y)^n=\sum ^n_{k\mathop=0}\frac{n!}{k!(n-k)!}x^{n-k}y^k[/tex]

In this case we have the polynomial

[tex](3x-y)^{17}[/tex]

to get the term:

[tex]x^4y^{13}[/tex]

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

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

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

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