If a-2 b-3 c-0- prove that a3-8 b3-27 c3-18 a b c

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Polynomials

If a+2 b+3 c=...

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If a+2b+3c=0,prove that a³+8b³+27c³=18abc

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{(a + 2 b - 3 c)}^{3} - a^{3} - 8 b^{3} + 27 c^{3}

27 a^{3} + 8 b^{3} - 27 c^{3} + 18 a b c

a^{3} + 8 b^{3} + c^{3} = 6 a b c

{(a - \frac{1}{2} b + \frac{1}{3} c)}^{3} - a^{3} + \frac{1}{8} b^{3} - \frac{1}{27} c^{3}

Question 36
Factorise:
(i) $a^{3} - 8 b^{3} - 64 c^{3} - 24 a b c$

(ii) $2 \sqrt{2} a^{3} + 8 b^{3} - 27 c^{3} + 18 \sqrt{2} a b c$

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