a^4b^2+a^2b^2+b^2因式分解

a^4b^2+a^2b^2+b^2
=a^4b^2+2a^2b^2+b^2-a^2b^2
=(a^2b+b)^2-(ab)^2
=(a^2b+b+ab)(a^2b+b-ab)
=b^2(a^2+a+1)(a^2-a+1)
a^4+a^2+1
=a^4+2a^2+1-a^2
=(a^2+1)^2-a^2
=(a^2+a+1)(a^2-a+1)
x^4+4
=x^4+4x^2+4-4x^2
=(x^2+2)^2-(2x)^2
=(x^2+2x+1)(x^2-2x+2)
x^4+324
=x^4+36x^2+18^2-36x^2
=(x^4+18)^2-(6x)^2
=(x^4+6x+18)(x-6x+18)