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## Homework Statement

Find the coefficient of [tex]x^{9}[/tex] [tex]y^{10}[/tex] in (3[tex]x^{3}[/tex] - 4[tex]y^{2}[/tex])[tex]^{8}[/tex]

## Homework Equations

The professor gave us a somewhat algebraic tactic or shortcut for solving these kinds of problems, mainly consisting of solving for each exponent. It can be somewhat tricky for me to explain with typing, but...

## The Attempt at a Solution

As per her suggested method, this is what I obtained:

C(8, k) (3[tex]x^{3}[/tex])[tex]^{8-k}[/tex] * ([tex]-4^{2}[/tex])[tex]^{k}[/tex]

3(8 - k) = 9, 2k = 10. Thus k = 5 and 8 - k = 3.

This gives me the answer C(8,5) * [tex]3^{3}[/tex] * [tex](-4)^{5}[/tex].

But her answer key in the provided review paper claims the answer is actually

C(8,3) * [tex]3^{3}[/tex] * [tex](-4)^{5}[/tex]

Have I done something wrong or is her answer incorrect? My text doesn't support her method and she is currently unavailable to assist me.

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