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Factorize: 27 x^3-y^3-z^3-9x y z...

Factorize: `27 x^3-y^3-z^3-9x y z`

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Verified by Experts

The given expression `27x^³+y^³+z^³-9xyz` can be written as`(3x)^³+(y)^³+(z)^³ - 3(3x)(y)(z)`
We can write: `(3x)^³+(y)^³+(z)^²-3(3x)(y)(z)= (3x + y + z)[(3x)^²+(y)^²+(z)^²-(3x)(y)-yz-(z)(3x)]`
Hence, `27x^³+y^³+z^³-9xyz=(3x+y+z)(9x^²+y^²+z^²-3xy- yz-3zx)`
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