Question

`1/27 x^3 - y^3 + 125z^3 + 5xyz`

Answer 1

`1/27 x^3 - y^3 + 125z^3 + 5xy`

`= (x/3)^3 + (-y)^3 + (5z)^3 - 3 xx x/3 (-y)(5z)`

`= (x/3 + (-y) + 5z)((x/3)^2 + (-y)^2 + (5z)^2 - x/3 (-y)- (-y)5z - 5z (x/3))`

`= (x/3 - y + 5z)(x^2/9 + y^2 + 25z^2 + (xy)/3 + 5xyz - 5/3 zx)`

`∴ 1/27 x^3 - y^3 + 125z^3 + 5xyz = (x/3 - y + 5z)(x^2/9 + y^2 + 25z^2 + (xy)/3 + 5yz - 5/3 zx)`