a + 2 b is equal to 5 prove that a 3 + 8b^3 + 30ab equal to 125
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(a+2b)=5............................(1)
we are asked to prove a³+8b³+30ab →(This is similar to the form [(a+b)³=a³+b³+3a²b+3ab²])
hence by cubing both sides of (1)
(a+2b)³=5³
(a³+8b³+6a²b+12ab²)=125 [using formula→(a+b)³=a³+b³+3a²b+3ab²]
(a³+8b³+6ab(a×2b))=125
(a³+8b³+6ab×5)=125 [substituting value for (a×2b)=5]
(a³+8b³+30ab)=125 : ║Hence proved║
we are asked to prove a³+8b³+30ab →(This is similar to the form [(a+b)³=a³+b³+3a²b+3ab²])
hence by cubing both sides of (1)
(a+2b)³=5³
(a³+8b³+6a²b+12ab²)=125 [using formula→(a+b)³=a³+b³+3a²b+3ab²]
(a³+8b³+6ab(a×2b))=125
(a³+8b³+6ab×5)=125 [substituting value for (a×2b)=5]
(a³+8b³+30ab)=125 : ║Hence proved║
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