Question

Expand using binomial theorem(4x-7y)^4

Answer 1

Recall that the binomial theorem states that:

`(a+b)^n=\sum ^n_(k=0){\binom{n}{k}}a^(n-k)b^k\text{.}`

Then:

`(4x-7y)^4=\sum ^4_(k=0){\binom{4}{k}}(4x)^(4-k)(-7y)^k\text{.}`

Therefore:

`\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}`