Question

If a + 2b = 5; then show that : a³ + 8b³ + 30ab = 125.

Answer 1

Given that a + 2b = 5 

We need to find a³ + 8b³ + 30ab 

Now consider the cube of a + 2b 

( a + 2b )³ = a³ + (2b)³ + 3 × a × 2b × ( a + 2b )

( a + 2b )³ = a³ + 8b³ + 6ab × ( a + 2b )

5³ = a³ + 8b³ + 6ab × 5       [ ∵ a + 2b = 5 ]

125 = a³ + 8b³ + 30ab

Thus the value of a³ + 8b³ + 30ab is 125.