Coefficient of Power of x Using Difference of Squares With Unmatched Powers

To find the coefficient of  
  in the expansion of  
  notice that  
Write the question as  
We are only interested in the coefficient of  
  so ignore any powers of  
  higher than  
\[\begin{equation} \begin{aligned} (3-x)^6(3+x)^4 &= (9-6x_x^2)(9-x^2)^4 \\ &= (9-6x+x^2)({}^4C_09^4(-x^2)^0+{}^4C_1 9^3(-x^2)^1+{}^4C_2 9^2(-x^2)^2+ higher \; powers \; of \; x) \\ &= (9-6x+x^2)(6561-2916x^2+486x^4 + higher \; powers \; of \; x ) \end{aligned} \end{equation}\]

The only contributions to the coefficient of  
  are from  
\[x^2 \times -2916 x^2\]
\[9 \times 486x^4=4374x^4\]
. The coefficient is  

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