Question

分解因式(x2+xy+y2)2-4xy(x2+y2)=?

Answer 1

解 原式=[(x+y)2-xy]2-4xy[(x+y)2-2xy]．令x+y=u,xy=v,则
原式=(u2-v)2-4v(u2-2v)
=u4-6u2v+9v2
=(u2-3v)2
=(x2+2xy+y2-3xy)2
=(x2-xy+y2)2．