The value of $$\left(x^{\frac{2}{3}} - x^{\frac{1}{3}}y^{\frac{1}{3}} + y^{\frac{2}{3}}\right)\left(x^{\frac{1}{3}} + y^{\frac{1}{3}}\right)$$​ is

Correct option is D

​Given:

​$$(x^{2/3} - x^{1/3}y^{1/3} + y^{2/3})(x^{1/3} + y^{1/3})$$​​

Solution:​ 

​$$(x^{2/3} - x^{1/3}y^{1/3} + y^{2/3})(x^{1/3} + y^{1/3})$$​​

$$=(x^{2/3})(x^{1/3}) + (x^{2/3})(y^{1/3}) - (x^{1/3}y^{1/3})(x^{1/3}) - (x^{1/3}y^{1/3})(y^{1/3}) + (y^{2/3})(x^{1/3}) + (y^{2/3})(y^{1/3})$$

 $$=x + \{x^{2/3} y^{1/3}\} - \{x^{2/3} y^{1/3}\} - \{x^{1/3} y^{2/3}\} + \{x^{1/3} y^{2/3}\} + y\\ \ \\ = x + y$$ 

Alternate Method: 

Identity ; 

​$$(x + y)^3 = (x+y)(x^2 - xy+y^2)$$ 

Comparing this with the expression we get 

​$$(x^{2/3} - x^{1/3}y^{1/3} + y^{2/3})(x^{1/3} + y^{1/3}) \\ \ \\ = (x+y)^{3 \times \frac 1 3} \\ \ \\ =x+y$$​​