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

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The coefficient of the term \(x^4y^3\) in the expansion of \((3x-2y)^7\) is calculated using the multinomial coefficient. The solution involves computing \({7\choose4,3}(3x)^4(-2y)^3\), which simplifies to \(35(81x^4)(-8y^3)\). This results in \(-22,680x^4y^3\). Therefore, the coefficient is \(-22,680\). The discussion highlights the contributions of members who provided correct solutions.
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Consider $(3x-2y)^7$. What is the coefficient of the $x^4y^3$ term?

 
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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]
 

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