`a)`
`(x + y + z)^3`
`= [(x + y)+ z]^3`
`= (x + y)^3 + 3(x + y)^2z + 3(x + y)z^2 + z^3`
`= x^3 + 3x^2y + 3xy^2 + y^3 + 3(x + y)^2z + 3(x + y)z^2 + z^3`
`= x^3 + y^3 + z^3 + 3xy(x + y) + 3(x + y)^2z + 3(x + y)z^2 `
`= x^3 + y^3 + z^3 + 3(x + y)[xy + z(x + y + z)]`
`= x^3 + y^3 + z^3 + 3(x + y)(y + z)(z + x)`
`b)`
`(x + y + z)^3 - x^3 - y^3 - z^3 `
`= [(x + y)+ z]^3 - x^3 - y^3 - z^3 `
`= (x + y)^3 + 3(x + y)^2z + 3(x + y)z^2 + z^3 - x^3 - y^3 - z^3 `
`= x^3 + 3x^2y + 3xy^2 + y^3 + 3(x + y)^2z + 3(x + y)z^2 + z^3 - x^3 - y^3 - z^3 `
`= x^3 + y^3 + z^3 + 3xy(x + y) + 3(x + y)^2z + 3(x + y)z^2 - x^3 - y^3 - z^3 `
`= x^3 + y^3 + z^3 + 3(x + y)[xy + z(x + y + z)] - x^3 - y^3 - z^3 `
`= x^3 + y^3 + z^3 + 3(x + y)(y + z)(z + x) - x^3 - y^3 - z^3 `
`= 3(x + y)(y + z)(z + x)`
