(m ^2 + 6 n )^2

To expand the given expression \((m^2 + 6n)^2\), we can use the formula for squaring a binomial:

\((a + b)^2 = a^2 + 2ab + b^2\)

In this case, let \(a = m^2\) and \(b = 6n\):

\((m^2 + 6n)^2 = (m^2)^2 + 2(m^2)(6n) + (6n)^2\)

Expanding further:

\(m^4 + 12m^2n + 36n^2\)

So, \((m^2 + 6n)^2\) simplifies to \(m^4 + 12m^2n + 36n^2\).