Question

Use the Binomial Theorem to expand (3n+4m)8. What is the coefficient of the fifth term, when written in standard form?

Answer 1

Binom Formula $\displaystyle (a+b)^n=\displaystyle \sum^{n}_{k=0}C^k_na^{n-k}b^k$

where $a=3n;~~ b=4m$ and we find the coefficient of the fifth term.

$C^4_8(3n)^{8-4}(4m)^4=\dfrac{8!}{4!4!}\cdot 3^4\cdot n^4\cdot 4^4\cdot m^4=12^4\cdot70m^4n^4$

coefficient is equal to $70\cdot 12^4=1451520$