Find the coefficient of x^5 for the expression: (1-x)^6(2x+3)^4 .. The answer provided is -222.... thanks...

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- Mar 6th 2011, 09:05 PMMichaelLightBinomial expansion
Find the coefficient of x^5 for the expression: (1-x)^6(2x+3)^4 .. The answer provided is -222.... thanks...

- Mar 6th 2011, 11:20 PMabhishekkgp
one way would be to differentiate this 5 times and then put x=0.

the other method is:

[coefficient of x^0 in (1-x)^6]*[coefficient of x^5 in (2x+3)^4] + [coefficient of x^1 in (1-x)^6]*[coefficient of x^4 in (2x+3)^4]+...+[coefficient of x^5 in (1-x)^6]*[coefficient of x^0 in (2x+3)^4]

for this you can use binomial theorem.