Find the coefficient of the term containing y ^9 in the expansion of (−x + 2y) ^12 .

Answer 1

Hi Jonothan,

Thanks for your question!

First, for simplicity, I'm going to redefine my variables. Let's let A = -x and B = 2y. Then, our binomial power is just (A+B)¹². I'd like to expand out this new expression and find the term that contains B⁹. According to the binomial theorem, this term will be ₁₂C₉ A³B⁹, where _nC_k = n! / (k! (n-k)!).

Now I'm going to plug back in my original variables into this term, so that ₁₂C₉ A³B⁹ becomes ₁₂C₉ (-x)³(2y)⁹ or, simplifying, -1*₁₂C₉ *2⁹x³y⁹. Thus, the coefficient of the term that contains y⁹ for the original binomial power is -1*₁₂C₉ *2⁹ = -112640. This is the final answer.