Prove that a3 + b3 + 8c3 = 6abc.

If a + b + 2c = 0, prove that a³ + b³ + 8c³ = 6abc.

Answer :

It is given that

a + b + 2c = 0

We can write it as

a + b = – 2c

By cubing on both sides

(a + b)³ = (-2c)³

Expanding using formula

a³ + b³ + 3ab (a + b) = -8c³

Substituting the value of a + b

a³ + b³ + 3ab (-2c) = -8c³

So we get

a³ + b³ + 8c³ = 6abc

Hence, it is proved.

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