Question

If a + 2b is equal to 5 then show that a raise to power 3 + 8b to the power 3 + 30ab is equal to 125

Answer 1

Formula to be used :
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(x + y) ³ = x³ + y³ + 3xy(x+y).
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(a +2b) = 5

Cubing both sides we get,
¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯
(a +2b) ³ = 5³

or,
(a) ³ + (2b)³ + 3a.2b(a+2b) =125

or,
a³ + 8b³ + 6ab×5 =125
( since a+2b=5)

or,
a³ + 8b³ +30ab = 125 (proved)