Question

分解因式 (x+y)4+x4+y4

Answer 1

(x+y)^4+x^4+y^4

=(x+y)^4+x^4+2x^2y^2+y^4-2x^2y^2

=(x+y)^4+(x^2+y^2)^2-2x^2y^2

=(x+y)^4+[(x^2+2xy+y^2)-2xy]^2-2x^2y^2

=(x+y)^4+[(x+y)^2-2xy]^2-2x^2y^2

=(x+y)^4+(x+y)^4-4xy(x+y)^2+4x^2y^2-2x^2y^2

=2(x+y)^4-4xy(x+y)^2+2x^2y^2

=2[(x+y)^4-2xy(x+y)^2+x^2y^2]

=2[(x+y)^2-xy]^2

=2(x^2+2xy+y^2-xy)^2

=2(x^2+xy+y^2)^2