Answer
$m^4+2m^3-3m^2-4m+4$
Work Step by Step
Using $(a+b+c)^2=a^2+b^2+c^2+2ab+2ac+2bc$ or the square of a multinomial, then,
\begin{array}{l}
(m^2+m-2)^2
\\=
(m^2)^2+(m)^2+(-2)^2+2(m^2)(m)+2(m^2)(-2)+2(m)(-2)
\\=
m^4+m^2+4+2m^3-4m^2-4m
\\=
m^4+2m^3+(m^2-4m^2)-4m+4
\\=
m^4+2m^3-3m^2-4m+4
.\end{array}
