Question

if a+2b=5 show that a^3+8b^3+30ab=125

Answer 1

a+2b=5
(a+2b)^3=5^3
a^3+8b^3+30ab=125
hence proved.
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Answer 2

Hope u like my process,
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Here we go,

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)__
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Hope u got it.

Proud to help you.