解：?$Q=(\mathrm {m^2}+1-m)(\mathrm {m^2}+1+m)=(\mathrm {m^2}+1)^2-\mathrm {m^2}$?
?$=m^4+2\ \mathrm {m^2}+1-\mathrm {m^2}=m^4+\mathrm {m^2}+1$?
?$P=[(m+1)(m-1)]^2=[\mathrm {m^2}-1]^2=m^4-2\ \mathrm {m^2}+1$?
∵?$m≠0$?
∴?$\mathrm {m^2}＞0$?
∴?$Q-P=m^4+\mathrm {m^2}+1-m^4+2\ \mathrm {m^2}-1=3\ \mathrm {m^2}＞0$?
∴?$Q＞P$?
