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Find the cube of each of the following b...

Find the cube of each of the following binomial expressions: (i) `1/x+y/3` (ii) `3/x-2/(x^2)`

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(i) `1/x+y/3`
`(1/x+y/3)^3=(1/x)^3+(y/3)^3+3\(1/x)\(y/3)\(1/x+y/3)`
`=1/x^3+y^3/(27)+y/x\(1/x+y/3)`
`=1/x^3+y^3/(27)+(y/x)xx(1/x)+(y/x)xx(y/3)`
`=1/x^3+y^3/(27)+y/x^2+y^2/(3x)`

(ii) `3/x-2/(x^2)`
` (3/x-2/(x^2))^3=(3/x)^3-(2/x^2)^3-3\(3/x)\(2/x^2)\(3/x-2/x^2)`
`=(27)/x^3-8/x^6-3xx(3/x)xx2/x^2\(3/x-2/x^2)`
`=(27)/x^3-8/x^6-(18)/x^3\(3/x-2/x^2)`
`=(27)/x^3-8/x^6-(54)/x^4+(36)/x^5`
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