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प्रश्न
Factorise:
27x3 + y3 + z3 – 9xyz
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उत्तर
It is known that,
x3 + y3 + z3 − 3xyz = (x + y + z) (x2 + y2 + z2 − xy − yz − zx)
∴ 27x3 + y3 + z3 – 9xyz = (3x + y + z)(3x)2 + (y)2 + (z)2 – (3x)y – yz – z(3x)
= (3x + y + z)(3x)2 + y2 + z2 – 3xy – yz – 3xz
= (3x + y + z)(9x2 + y2 + z2 – 3xy – yz – 3xz)
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