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

Thread starter Jameson
Start date Jun 11, 2012

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SUMMARY

The coefficient of the term $x^4y^3$ in the expansion of $(3x-2y)^7$ is $-22,680$. This was determined using the multinomial coefficient ${7\choose4,3}$ along with the respective powers of $3x$ and $-2y$. The calculation involves multiplying $35$ (the multinomial coefficient) by $81x^4$ and $-8y^3$, resulting in the final coefficient of $-22,680$.

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Jun 11, 2012

Jameson

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

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Jun 17, 2012

Jameson

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Gold Member

MHB

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]