因式分解:x^4-2x^4y+x^4y^2-2x^2+y^2-2x^2y^2+2y+1
题目
因式分解:x^4-2x^4y+x^4y^2-2x^2+y^2-2x^2y^2+2y+1
答案
x^4-2x^4y+x^4y^2-2x^2+y^2-2x^2y^2+2y+1
=x^4y^2-2x^2y^2+y^2-2x^4y+2y+x^4-2x^2+1
=y^2(x^4-2x^2+1)-2y(x^4-1)+x^4-2x^2+1
=y^2(x^2-1)^2-2y(x^2+1)(x^2-1)+(x^2-1)^2
=(x^2-1)(x^2y^2-y^2-2x^2y-2y+x^2-1)
=(x^2-1)[x^2(y^2-2y+1)-(y^2+2y+1)]
=(x-1)(x+1)[(xy-x)^2-(y+1)^2]
=(x-1)(x+1)(xy-x-y-1)(xy-x+y+1)
举一反三
我想写一篇关于奥巴马的演讲的文章,写哪一篇好呢?为什么好
最新试题
热门考点