Answer:
Recall that the binomial theorem states that:
[tex](a+b)^n=\sum ^n_{k=0}{\binom{n}{k}}a^{n-k}b^k\text{.}[/tex]Then:
[tex](4x-7y)^4=\sum ^4_{k=0}{\binom{4}{k}}(4x)^{4-k}(-7y)^k\text{.}[/tex]Therefore:
[tex]\begin{gathered} (4x-7y)^4={\binom{4}{0}(4x)^{4-0}(-7y)^0}+{\binom{4}{1}(4x)^{4-1}(-7y)^1}+{\binom{4}{2}(4x)^{4-2}(-7y)^2} \\ +{\binom{4}{3}(4x)^{4-3}(-7y)^3+{\binom{4}{4}(4x)^{4-4}(-7y)^4\text{.}}} \end{gathered}[/tex]