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Question
x3 - 8y3 + 27z3 +18xyz
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Solution
= x3 + (-2 y )3 + (3z )3 - 3 × x × (-2 y )(3z )
= (x + (-2 y ) + 3z )(x2 + (-2y)2 + (3z)2 - x (-2y) - (-2y)(3z) - 3z (x )) [∵ a3 + b3 + c3 - 3abc = (a + b + c)(a2 + b2 + c2 - ab - bc - ca )]
= ( x - 2 y + 3z )(x2 + 4 y2 + 9z2 + 2xy + 6 yz - 3zx)
∴ x3 - 8y3 + 27z3 +18xyz = ( x - 2 y + 3z )(x2 + 4 y2 + 9z2 + 2xy + 6 yz - 3zx)
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