please expand (1/x + y/3) (whole cube)
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we have to expand (1/x + y/3)³
we know,
(a + b)³ = (a + b)²(a + b)
= (a² + 2ab + b²)(a + b)
= a³ + 2a²b + ab² + a²b + 2ab² + b³
= a³ + 3a²b + 3ab² + b³
so, (1/x + y/3)³ = (1/x)³ + 3(1/x)²(y/3) + 3(1/x)(y/3)² + (y/3)³
= 1/x³ + y/x² + y²/3x + y³/27
hence, (1/x + y/3)³ = 1/x³ + y/x² + y²/3x + y³/27
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