9m^2-25n^4
=(3m+5n)(3m-5n)
(x+y)^4-(x-y)^4
={(x+y)^2+(x-y)^2}{(x+y)^2-(x-y)^2}
=(2x^2+2y^2)4xy
=8xy(x^2+y^2)
2ab-(ab)^2-1+c^2
=c^2-(ab-1)^2
=(c+ab-1)(c-ab+1)
ab(c^2+d^2)+cd(a^2+b^2)
=abc^2+abd^2+cda^2+cdb^2
=abc^2+cdb^2+abd^2+cda^2
=bc(ac+bd)+ad(bd+ac)
=(bd+ac)(ad+bc)