分解因式: ①x2y2-5x2y-6x2 ②(p2+q2)2-4p2q2 ③(a-b)4-3(a-b)2-10 ④x2-y2+4y-4.

问题描述:

分解因式:
①x2y2-5x2y-6x2
②(p2+q22-4p2q2
③(a-b)4-3(a-b)2-10   
④x2-y2+4y-4.

①x2y2-5x2y-6x2 =x2(y2-5y-6)=x2(y-6)(y+1);
②(p2+q22-4p2q2=(p2+q2+2pq)(p2+q2-2pq)=(p+q)2(p-q)2
③(a-b)4-3(a-b)2-10=[(a-b)2-5][(a-b)2+2]; 
④x2-y2+4y-4=x2-(y2-4y+4)=x2-(y-2)2=(x+y-2)(x-y+2).