Question

分解因式：a3b-ab3+a2+b2+1=

Answer 1

a3b-ab3

=ab(a^2-b^2)

=ab(a+b)(a-b)

=[a(a+b)][b(a-b)]

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

a3b-ab3+a2+b2+1

=(a^2+ab)(ab-b^2)+[(a^2+ab)-(ab-b^2)]+1

令a^2+ab=X,ab-b^2=Y

=XY+X-Y+1

这一步有点问题,无法再展开

应该是

XY+X-Y-1

=(X-1)(Y+1)

那么

a3b-ab3+a2+b2-1

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