试题:
因式分解.
(1)x4+x2y2+y4
(2)-a2-b2+2ab+4
(3)x4+5x2-6
(4)(x+y)(x+y+2xy)+(xy+1)(xy-1)
因式分解 2016-05-17

答案:

我来补答
(1)x4+x2y2+y4
=x4+2x2y2+y4-x2y2
=(x2+y22-x2y2
=(x2+y2+xy)(x2+y2-xy);

(2)-a2-b2+2ab+4,
=4-(a-b)2
=(2+a-b)(2-a+b);

(3)x4+5x2-6,
=(x2+6)(x2-1),
=(x2+6)(x-1)(x+1);

(4)(x+y)(x+y+2xy)+(xy+1)(xy-1).
=(x+y)2+2xy(x+y)+(xy)2-1.
=(x+y+xy)2-1.
=(x+y+xy+1)(x+y+xy-1).
 
 
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