m+n=24then(m-16)^3+(n-8)^3=
You asked:
Given \(m + n = 24\) evaluate the expression \({\left( m - 16 \right)}^{3} + {\left( n - 8 \right)}^{3}\).
MathBot Answer:
\[\left(m - 16\right)^{3} + \left(n - 8\right)^{3} = \left(8 - n\right)^{3} + \left(n - 8\right)^{3}\]
\[m + n = 24\]Solve for $m$: \[m = 24 - n\]Substitute $m$ into the given expression: $$\begin{aligned}\left(m - 16\right)^{3} + \left(n - 8\right)^{3} &= \left(n - 8\right)^{3} + \left(-16 + 24 - n\right)^{3} \\ \left(m - 16\right)^{3} + \left(n - 8\right)^{3} &= \left(8 - n\right)^{3} + \left(n - 8\right)^{3}\end{aligned}$$