早教吧作业答案频道 -->数学-->
因式分解:x^4+y^4+(x+y)^4-2
题目详情
因式分解:x^4+y^4+(x+y)^4-2
▼优质解答
答案和解析
x^4+y^4+(x+y)^4-2
=x^4+y^4+(x^2+2xy+y^2)^2 -2
=x^4+y^4+[(x^2+y^2)+2xy]^2 -2
=x^4+y^4+(x^2+y^2)^2+4xy(x^2+y^2)+(2xy)^2 -2
=(x^2+y^2)^2-2x^2y^2+(x^2+y^2)^2+4xy(x^2+y^2)+(2xy)^2 -2
=(x^2+y^2)^2+2x^2y^2+(x^2+y^2)^2+4xy(x^2+y^2) -2
=2[(x^2+y^2)^2+2xy(x^2+y^2)+x^2y^2] -2
=2(x^2+y^2+xy)^2-2
=2[(x^2+y^2+xy)^2-1]
=2(x^2+y^2+xy+1)(x^2+y^2+xy-1)
=x^4+y^4+(x^2+2xy+y^2)^2 -2
=x^4+y^4+[(x^2+y^2)+2xy]^2 -2
=x^4+y^4+(x^2+y^2)^2+4xy(x^2+y^2)+(2xy)^2 -2
=(x^2+y^2)^2-2x^2y^2+(x^2+y^2)^2+4xy(x^2+y^2)+(2xy)^2 -2
=(x^2+y^2)^2+2x^2y^2+(x^2+y^2)^2+4xy(x^2+y^2) -2
=2[(x^2+y^2)^2+2xy(x^2+y^2)+x^2y^2] -2
=2(x^2+y^2+xy)^2-2
=2[(x^2+y^2+xy)^2-1]
=2(x^2+y^2+xy+1)(x^2+y^2+xy-1)
看了 因式分解:x^4+y^4+(...的网友还看了以下：
求下列曲线所围成的图形的面积,x^2+y^2=4,y=(x^2/3) 2020-05-13 …
高一集合一道集合A={(x,y)|x^2+y^2=4},B={(x,y)|(x-3)^2+(y-4 2020-07-29 …
{x^2+y^2=12x+y=5{x^2-y^2+x-y-6=0x^2-y^2-x+y-4=0{x^ 2020-10-31 …
若双曲线x^2/4-y^2/5=1与椭圆x^2/z^2+y^2/16=1有公共焦点,且z>0,则z= 2020-10-31 …
(1).-3ma^3+6ma^-12ma(2).x^6n+2+2x^3n+2+x^2(3).5(x- 2020-10-31 …
设(x+√(x^2+1))(y+√(y^2+4))=9则x√(y^2+4)+y√(x^2+1)=? 2020-10-31 …
[(x+y)^2-(x-y)^2]/(2xy)=?(x+2)^2-(x+2)(x-2)=?(-0.5 2020-11-01 …
数学题(急)(1)7x^2-63(2)a^3-a(3)3a^2-3b^2(4)y^2-9(x+y)^ 2020-11-01 …
4道分解因式.2道分解计算(初二)分解因式1.x^4(x-y)+y^4(y-x)2.4-12(x-y 2020-11-07 …
若(x^2+y^2)^4-8(x^2+y^2)^2+16=0求x^2+y^2的值错解：设(x^2+y 2021-01-07 …