Solution to $(3x-2y)^7$ - Coefficient of $x^4y^3$

[Jameson]

Consider $(3x-2y)^7$. What is the coefficient of the $x^4y^3$ term?

 

[Jameson]

Congratulations to the following members for their correct solutions:

1) Sudharaka
2) veronica1999
3) soroban

Solution (from soroban):

[sp]$${7\choose4,3}(3x)^4(-2y)^3 \;=\;35(81x^4)(-8y^3) \;=\;-22,680x^4y^3$$

The coefficient is:$$\, \,-22,680.$$[/sp]