`1, x^4+y^4+(x+y)^4`
`=(x^2+y^2)^2-2x^2y^2+(x+y)^4`
`=[(x+y)^2-2xy]^2+[(x+y)^2-2xy][(x+y)^2+2xy]`
`=[(x+y)^2-2xy][(x+y)^2-2xy+(x+y)^2+2xy]`
`=2(x^2+2xy+y^2-2xy)(x+y)^2`
`=2(x^2+y^2)(x+y)^2`
`2, x^7+x^2+1`
`=x^7-x+x^2+x+1`
`=x(x^6-1)+(x^2+x+1)`
`=x(x^3-1)(x^3+1)+(x^2+x+1)`
`=x(x-1)(x^2+x+1)(x^3+1)+(x^2+x+1)`
`=(x^2+x+1)[x(x-1)(x^3+1)+1]`
`=(x^2+x+1)[(x^2-x)(x^3+1)+1]`
`=(x^2+x+1)(x^6+x^2-x^4-x+1)`