What is the ninth term in the binomial expansion of (x – 2y)13?

The ninth term uses the exponent 8 on the second part, so it is \(\binom{13}{8}x^{13-8}(-2y)^8\). Since \(\binom{13}{8}=1287\) and \((-2)^8=256\), the term is \(1287\cdot256x^5y^8=329{,}472x^5y^8\). The sign is positive because the exponent on \(-2y\) is even, so the answer is 329,472x⁵y⁸.

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