因式分解x4+y4+(x+y)4
热心网友
解：x^4+y^4+(x+y)^4 =(x^4+y^4+2x^2y^2)-2x^2y^2+(x+y)^4 =(x^2+y^2)^2-2x^2y^2+(x^4+4x^3y+6x^2y^2+4xy^3+y^4) =(x^2+y^2)^2+(x^4+2x^2y^2+y^4)+(4x^3+2x^2y^2+4xy^3) =(x^2+y^2)^2+(x^2+y^2)^2+4(x^2+y^2)xy+2x^2y^2 =2(x^2+y^2)^2+4xy(x^2+y^2)+2x^2y^2 =2[(x^2+y^2)^2+2xy(x^2+y^2)+x^2y^2] =2(x^2+xy+y^2)^2又解：原式＝2x^4+4x^3*y+6x^2*y^2+4xy^3+y^4 =2[(x^4+2x^2*y^2+y^4)+2(x^3*y+xy^3)+x^2*y^2] =2[(x^2+y^2)^2+2xy(x^2+y^2)+(xy)^2] =2(x^2+xy+y^2)^2。
热心网友
接原式=4x+4y+4x+4y=8x+8y=8(x+y)
热心网友
x4+y4+(x+y)4 解原式=4（x+y)+(x+y)4 =4(x+y)[1+1] =8(x+y)
热心网友
(x+y)8