Question

请教一道因式分解题(1-x^2)(1-b^2)-4ab

Answer 1

(1-a^2)(1-b^2)-4ab

=a^2b^2-a^2-b^2+1-4ab

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

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

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

=(ab-1-a-b)(ab-1+a+b).