(x-2/3*y)³,Expand it, using suitable identities.
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Solution :
*****************************************
We know the algebraic identity,
(a-b)³ = a³- 3a²b + 3ab² - b³
*****************************************
Here ,
a = x , b = 2y/3 ,
Now ,
( x - 2y/3 )³
= x³-3*x²*(2y/3)+3*x*(2y/3)² - (2y/3)³
= x³ - (3x²*2y)/3 + ( 3x*4y²)/9 - 8y³/27
= x³ - 2x²y + 4xy²/3 - 8y³/27
••••
*****************************************
We know the algebraic identity,
(a-b)³ = a³- 3a²b + 3ab² - b³
*****************************************
Here ,
a = x , b = 2y/3 ,
Now ,
( x - 2y/3 )³
= x³-3*x²*(2y/3)+3*x*(2y/3)² - (2y/3)³
= x³ - (3x²*2y)/3 + ( 3x*4y²)/9 - 8y³/27
= x³ - 2x²y + 4xy²/3 - 8y³/27
••••
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