To expand \((-6m - n)^2\), you can use the formula for the square of a binomial, which states that \((a - b)^2 = a^2 - 2ab + b^2\).
In this case, let \(a = -6m\) and \(b = n\).
Now, apply the formula:
\[ (-6m - n)^2 = (-6m)^2 - 2(-6m)(n) + n^2 \]
Calculate each term:
- \((-6m)^2 = 36m^2\)
- \(-2(-6m)(n) = 12mn\)
- \(n^2\)
Putting it all together:
\[ (-6m - n)^2 = 36m^2 + 12mn + n^2 \]
Thus, the expanded form is:
\[ 36m^2 + 12mn + n^2 \]