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

1 Answer
Jan 4, 2016

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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