Factorize
(p-q) ³+(q-3)³+(r-p) ³
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{ (p-q) ³+(q-3)³+(r-p) ³ }
= { p³-q³-3(p)(q)(p-q) + (q³-27-3(q)(3)(q-3)) + (r³-p³-3(r)(p)(r-p)) }
= p³-q³-3p²q+3pq² + (q³ -27-9q²+9) + ( r³-p³-3r²p+3rp²)
= p³-q³-3p²q+3pq² + q³-27-9q²+27q+ r³-p³-3r²p+3rp²
= p³-p³-q³+q³-r³-3p²q-3pq²-3r²p+3rp²-9q²+27q-27
= -r³-3p²q-3pq²-3r²p+3rp²-9q²+27q-27
= { p³-q³-3(p)(q)(p-q) + (q³-27-3(q)(3)(q-3)) + (r³-p³-3(r)(p)(r-p)) }
= p³-q³-3p²q+3pq² + (q³ -27-9q²+9) + ( r³-p³-3r²p+3rp²)
= p³-q³-3p²q+3pq² + q³-27-9q²+27q+ r³-p³-3r²p+3rp²
= p³-p³-q³+q³-r³-3p²q-3pq²-3r²p+3rp²-9q²+27q-27
= -r³-3p²q-3pq²-3r²p+3rp²-9q²+27q-27
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