因式分解(x^2+xy+y^2)-4xy(x^2+y^2)
1个回答
展开全部
(x^2+xy+y^2)^2-4xy(x^2+y^2)
=[(x^2+2xy+y^2)-xy]^2-4xy[(x^2+y^2+2xy)-2xy]
=[(x+y)^2-xy]^2-4xy[(x+y)^2-2xy]
=(x+y)^4-2xy(x+y)^2+(xy)^2-4xy(x+y)^2+8(xy)^2
=(x+y)^4-6xy(x+y)^2+9(xy)^2
=[(x+y)^2]^2-6xy(x+y)^2+9(xy)^2
=[(x+y)^2-3xy]^2
=(x^2+2xy+y^2-3xy)^2
=(x^2-xy+y^2)^2
=[(x^2+2xy+y^2)-xy]^2-4xy[(x^2+y^2+2xy)-2xy]
=[(x+y)^2-xy]^2-4xy[(x+y)^2-2xy]
=(x+y)^4-2xy(x+y)^2+(xy)^2-4xy(x+y)^2+8(xy)^2
=(x+y)^4-6xy(x+y)^2+9(xy)^2
=[(x+y)^2]^2-6xy(x+y)^2+9(xy)^2
=[(x+y)^2-3xy]^2
=(x^2+2xy+y^2-3xy)^2
=(x^2-xy+y^2)^2
已赞过
已踩过<
评论
收起
你对这个回答的评价是？
推荐律师服务：
若未解决您的问题，请您详细描述您的问题，通过百度律临进行免费专业咨询
