How do you use the binomial formula to find the coefficient of $u^(4)z^(15)$ in the expansion of $(3u+z)^19$ ?

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Answer 1 · 2016-03-17T15:23:46

313956

The coefficient of $a^rb^(n-r)$ in the expansion of $( a + b )^n$ is $nCn-r$ = $(n!)/((n-r)!r!)$

Here a = 3u, b = z, n = 19 and r = 4.

Answer is 19C4 X $3^4$ = $3^4$ (19.18.17.16(/(1.2.3.4) = 313956.

How do you use the binomial formula to find the coefficient of u^(4)z^(15)u^(4)z^(15) in the expansion of (3u+z)^19(3u+z)^19?