Expand the following `(i) (3a-2b)^(3) (ii) ((1)/(x)+(y)/(3))^(3)` (iii) `(4-(1)/(3x))^(2)`

Expand the following `(i) (3a-2b)^(3) (ii) ((1)/(x)+(y)/(3))^(3)` (iii

1.	Expand the following `(i) (3a-2b)^(3) (ii) ((1)/(x)+(y)/(3))^(3)` (iii) `(4-(1)/(3x))^(2)`
Answer» (i) Putting `(1)/(x)=a and (y)/(3)=b`, we get `((1)/(x)+(y)/(3))^3=(a+b)^3` ` =a^3+b^3+3ab(a+b)` `=((1)/(x))^3+((y)/(3))^3+3xx(1)/(x)xx(y)/(3)xx((1)/((x)+(y)/(3)))` `=(1)/(x^3)+(y^3)/(27)+(y)/(x)((1)/(x)+(y)/(3))` `=(1)/(x^3)+(y^3)/(27)+(y)/(x^2)+(y^2)/(3x)=(1)/(x^3)+(y)/(x^2)+(y^2)/(3x)+(y^3)/(27)`. (ii) Putting `4=a and (1)/(3x)=b`, we get `(4-(1)/(3x))^2=(a-b)^3` `a^3-b^3-3ab(a-b)` `=(4)^3-((1)/(3x))^3-3xx4xx(1)/(3x)xx(4-(1)/(3x))` `=64-(1)/(27x^3)-(16)/(x)+(4)/(3x^2)=64-(16)/(x)+(4)/(3x^2)-(1)/(27x^3)`