因式分解:a＾3b-ab＾3+a＾2+b＾2+1

Question

因式分解:a＾3b-ab＾3+a＾2+b＾2+1

Answer 1

a^3b-ab^3+a^2+b^2+1
=a^3b-a^2b^2+a^2b^2+ab-ab-ab^3+a^2+b^2+1
=a^3b-a^2b^2+ab+a^2b^2-ab^3+b^2+a^2-ab+1
=ab(a^2-ab+1)+b^2(a^2-ab+1)+1(a^2-ab+1)
=(ab+b^2+1)(a^2-ab-1)