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8x^{3} + 27y^{3} - 216z^{3} + 108xyz

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#### Solution

= (2x)^{3} + (3y )^{3} + (-6z )^{3} - 3(2x)(3y )(-6z )

= (2x + 3y + (-6z ))((2x)^{2} + (3y )^{2} + (-6z )^{2} - 2x × 3y - 3y (-6z ) - (-6z )2x)

= (2x + 3y - 6z )(4x^{2} + 9 y^{2} + 36z^{2} - 6xy +18 yz +12zx)

∴ 8x^{3} + 27 y^{3} - 216z^{3} +108xyz = (2x + 3y - 6z )(4x^{2} + 9 y^{2} + 36z^{2} - 6xy +18 yz +12zx)

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