If a + 2b = 5, prove that a3 + 8b3 + 30ab = 125.

If a + 2b = 5, prove that a³ + 8b³ + 30ab = 125.

Answer :

We know that

(a + 2b)³ = a³ + 8b³ + 3 (a) (2b) (a + 2b)

Substituting the values

5³ = a³ + 8b³ + 6ab (5)

By further calculation

125 = a³ + 8b³ + 30ab

Therefore, a³ + 8b³ + 30ab = 125.

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