Question

分解因式：（X+Y）的4次方+X的4次方+Y4次方

Answer 1

x^4+y^4+(x+y)^4 =x^4+y^4+x^4+y^4+4x^2y^2+4x^3y^2+2X^2y^2+4xy^3 =2x^4+2y^4+6x^2y^2+4x^3y+4xy^3 =2(x^4+y^4+3x^2y^2+2x^2y+2xy^3) =2[(x^4+2x^2y^2+x^4)+(2x^3y+2xy^3+x^2y^2] =2[(x^2+y^2)^2+2xy(x^2+y^2)+x^2y^2] =2(x^2+y^2+xy)^2