[數學]因式分解

Question

請問各位大大們解題的方法：(請附上詳解)謝謝大家，感激不盡
(1)4x^2y^2-x^2+2xy-y^2
(2)(a^2)(b^2)-4ab
(3)x^2y^2-x^2-y^2-6xy+4
(4)a^4+4a^2-b^2-2b+3

Answer 1

4x2y2 - x2 + 2xy - y2 = 4x2y2-(x2-2xy+y2 ) = 4x2y2-(x-y)2=[2xy - (x - y)][(2xy + (x - y)]=(2xy - x + y)(2xy + x - y)a2b2-4ab = (a2b2-4ab+4) - 4 = (ab-2)2 -22= (ab-2+2)(ab-2-2) = ab (ab - 4)x2y2-x2-y2-6xy+4 = (x2y2 - 4xy + 4) - (x2 + 2xy + y2)= (xy - 2)2 - (x + y)2 = (xy + x + y - 2)(xy - x - y - 2)a4+4a2-b2-2b+3 = (a4+4a2+4) - (b2+2b+1)= (a2 + 2)2 - (b + 1)2 = (a2 + b +3)(a2 - b +1)