Question

x的四次方+y的四次方+（y+x）的四次方 因式分解

Answer 1

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