How do you find the coefficient of x^6 in the expansion of #(2x+3)^10#?

1 Answer
Jan 4, 2016

Answer:

Calculate the binomial coefficient and appropriate powers of #2# and #3# to find that the required coefficient is:

#1088640#

Explanation:

#(2x+3)^10 = sum_(k=0)^10 ((10),(k)) 2^(10-k)3^k x^(10-k)#

The term in #x^6# is the one for #k=4#, so has coefficient:

#((10),(4)) 2^6*3^4#

#=(10!)/(4! 6!)*64*81#

#=(10xx9xx8xx7)/(4xx3xx2xx1)*64*81#

#=210*64*81 = 1088640#

Instead of calculating #((10),(4))#, you can pick it out from the appropriate row of Pascal's triangle...

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