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Expert: - 7/25/2010


Question
If a + 2*b = 5, show that:-
cube of a + 8*cube of b + 30*a*b = 125

Answer
It is known the 125 = 5*5*5 = 5³.
This means we need to show that (a+2b)³ = a³ + 8b³ + 30ab.

Now it is known that if we have (x+y)³, it is x³ + 3x²y + 3xy² + y³.
From this, it can be said that (a+2b)³ = a³ + 6a²b + 12ab² + 8b³.

This means we can say that  a³ + 8b³ + 30ab = a³ + 6a²b + 12ab² + 8b³.
The cubes cancel, and what's left is showing 30ab = 6a²b + 12ab².

Dividing this equation by ab gives 30 = 6a + 12b.

If we take a + 2b = 5 and multiply by 6, then we've got it since it gives us 6a + 12b = 30.  

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