$解:(1)(m+n)^{2}=(2+1)^{2}=3^{2}=9$
$m^{2}+2mn+n^{2}=2^{2}+2×2×1+1^{2}=9$
$(2)(m+n)^{2}=m^{2}+2mn+n^{2}$
$(3)当m=5,n=-2时,(m+n)^{2}=[5+(-2)]^{2}=3^{2}= 9$
$m^{2}+2mn+n^{2}=5^{2}+2×5×(-2)+(-2)^{2}=9$
$\ \ \ (2)中的结论仍成立$
$(4)m^{2}+2mn+n^2=(m+n)^2=(0.125+0.875)^{2}=1$