Factorise:

We have:

$m^{4}+2 m^{2} n^{2}+n^{4}=\left(m^{2}\right)^{2}+2 \times m^{2} \times n^{2}+\left(n^{2}\right)^{2}$

$=\left(m^{2}+n^{2}\right)^{2}$

$\therefore m^{4}+2 m^{2} n^{2}+n^{4}=\left(m^{2}+n^{2}\right)^{2}$