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Question
8x3 + 27y3 - 216z3 + 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 )(4x2 + 9 y2 + 36z2 - 6xy +18 yz +12zx)
∴ 8x3 + 27 y3 - 216z3 +108xyz = (2x + 3y - 6z )(4x2 + 9 y2 + 36z2 - 6xy +18 yz +12zx)
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