16x^4+24x^2+9a^2x^2+16ax+64 (x^2-2x)^2+2(x^2-2x)+1 m^2(m-1)-

16x^4+24x^2+9
=(4x^2+3)^2
=[(2x+√3i)(2x-√3i)]^2
a^2x^2+16ax+64
=(ax+8)^2
(x^2-2x)^2+2(x^2-2x)+1
=[(x^2-2x)+1]^2
=[(x-1)^2]^2
=(x-1)^4
m^2(m-1)-4(1-m)^2
=-[m^2(1-m)+4(1-m)^2]
=-{(1-m)[m^2+4(1-m)]}
=-[(1-m)(m^2-4m+4)]
=-[(1-m)(m-2)^2]
=(m-1)(m-2)^2
(a^2+b^2)(a+b)^2-(a^2-b^2)^2
=(a^2+b^2)(a+b)^2-(a+b)^2(a-b)^2
=(a+b)^2[(a^2+b^2)-(a-b)^2]
=(a+b)^2(a^2+b^2-a^2-b^2+2ab)
=2ab(a+b)^2