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ParthKohli
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ParthKohli
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I know this simplifies to\[\left(\dfrac{2}{3}x + \dfrac{5}{3}y\right)^3 + \rm blah\]

ParthKohli
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So for the first two terms, should I use \(a^3 + b^3 = (a + b)(a^2  ab + b^2)\)?

ParthKohli
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That'd make stuff very long.

hartnn
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its like
\((a+b)^3+(cb)^3(a+c)^3\)

ParthKohli
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Yeah. :

ParthKohli
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Wait, so\[(a + c)(a^2 + 2ab + b^2  (a+b)(c b) + c^2  2cb + b^2)  (a + c)^3\]

hartnn
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\(\large = 3(a+b)(a+c)(bc)\)

ParthKohli
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How did you get that?

ParthKohli
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It's correct, but is it some sort of identity taught?

hartnn
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ok, first take last 2 terms,
(cb)^3(a+c)^3 = ... ?
use A^3B^3 =...

hartnn
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not identity, you need to work that out...

hartnn
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its quite long though

ParthKohli
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\[a^3  b^3 = (a  b)(a^2 + ab + b^2)\]So here,\[= (b +a)(\cdots)\]Err

ParthKohli
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No shortcuts?

hartnn
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none that i can think of.

ParthKohli
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There's always a shortcut in exam questions. It's not like an Olympiad one.

hartnn
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then you must be having choices ?

ParthKohli
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No choices given. That's all.

ParthKohli
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:(

hartnn
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then i'll wait for someone to suggest a shortcut.....

ParthKohli
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OK, thanks for the support :)


some_someone
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I usually use that, but i don't know if its going to help you?

ParthKohli
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@hartnn Oh BTW, I found the solution.

hartnn
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any shortcuts ?


hartnn
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isn't that exactly what i told you ?

ParthKohli
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:P