Answer
$m^6 - 24 m^5 + 240 m^4 - 1280 m^3 + 3840 m^2 - 6144 m + 4096$
Work Step by Step
Using the Binomial Formula, the expression $
(m-4)^6
$ expands to
\begin{array}{l}
m^6(-4)^0
\dfrac{6}{1!}m^5(-4)^1+
\dfrac{6\cdot5}{2!}m^4(-4)^2+
\dfrac{6\cdot5\cdot4}{3!}m^3(-4)^3+\\
\dfrac{6\cdot5\cdot4\cdot3}{4!}m^2(-4)^4+
\dfrac{6\cdot5\cdot4\cdot3\cdot2}{5!}m^1(-4)^5+\\
\dfrac{6\cdot5\cdot4\cdot3\cdot2\cdot1}{6!}m^0(-4)^6
\\\\=
m^6 - 24 m^5 + 240 m^4 - 1280 m^3 + 3840 m^2 - 6144 m + 4096
\end{array}
