Question

Find the cube of the following binomials expression :

\[2x + \frac{3}{x}\]

Answer 1

In the given problem, we have to find cube of the binomial expressions

 Given  `(2x + 3/x)^3`

We shall use the identity  `(a+b)^3 = a^3+b^3 +3ab(a+b).`

Here `a = 2x,b = 3/x,`

By applying identity we get 

`(2x + 3/x)^3 = (2x)^3 +(3/x)^3 + 3 (2x) (3/x) (2x+3/x)`

`= 2x xx 2x  xx2x|+3/x xx3/x xx 3/x+18x/x (2x+3/x)`

`= 8x^3 +27/x^3 + (18x)/x (2x + 3/x)`

` = 8x^3 +27/x^3 + (18xx 2x) +(18 xx 3/x)`

`8^3+27/x^3 + 36x +54/x`

Hence cube of the binomial expression of  `(2x + 3/x) 8^3+27/x^3 + 36x +54/x`