Factorize: `x^6+y^6`

Explanation

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`x^6-y^6`
`(x^2)^3-(y^2)^3`
`(x^2-y^2)[(x^2)^2+(y^2)^2+(x^2xxy^2)]=(x-y)(x+y)(x^2+y^2+xy)(x^2+y^2-xy)`
Using identities
`a^2-b^2=(a+b)(a-b)` and `a^4+b^4+a^2b^2=(a^2+b^2+ab)(a^2+b^2-ab)`
Hence , `(x^6-y^6=(x-y)(x+y)(x^2+y^2+xy)(x^2+y^2-xy))`