Mathematics: What is the ninth term in the binomial expansion of (x-2y)^13

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What is the ninth term in the binomial expansion

dondre54

12.03.2022

$T_{9}=329472x^{5}y^8$

Step-by-step explanation:

$(x-2y)^{13}$

$T_{r+1}=nCr x^{n-r} y^r$

x is the first term in the given parenthesis and y is the second tern

r= 8, r+1=9 because we need to find 9th term

x is x and y is 2y. n is the exponent 13. plug in all the values

$T_{8+1}=13C8 x^{13-8} (2y)^8$

$T_{8+1}=13C8 x^{5} (2y)^8$

nCr= $\frac{n!}{r!(n-r)!}=\frac{13!}{8!(5!)=1287$

$T_{8+1}=1287x^{5} 256y^8$

$T_{9}=329472x^{5}y^8$

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