Question

Find the 2nd term in the expansion of (x+4y)^6

in simplest form.

Answer 1

`\textit{binomial expanded }2^(nd)\textit{ term for}\qquad (x+4y)^6\qquad \begin{cases} \stackrel{\textit{2nd term}}{k=1}\\ n=6 \end{cases} \\\\ \stackrel{\stackrel{coefficient}{\downarrow }}{\left(\cfrac{6!}{1!(6-1)!}\right)} \qquad \stackrel{\stackrel{\textit{first term factor}}{\downarrow }}{\left( x \right)^(6-1)} \qquad \stackrel{\stackrel{\textit{second term factor}}{\downarrow }}{\left( 4y\right)^1}\qquad \implies 6(x)^5(4y)^1\implies 24x^5y`