If x - y = 13 and xy = 25, then the value of $$x^2 - y^2$$ = ?

Given,

$$x - y = 13$$ and  $$xy = 25$$

$$=$$>  $$\left(x-y\right)^2=13^2$$

$$=$$>  $$x^2+y^2-2xy=169$$

$$=$$>  $$x^2+y^2+2xy-4xy=169$$

$$=$$>  $$\left(x+y\right)^2-4xy=169$$

$$=$$>  $$\left(x+y\right)^2-4\left(25\right)=169$$

$$=$$>  $$\left(x+y\right)^2-100=169$$

$$=$$>  $$\left(x+y\right)^2=269$$

$$=$$>  $$x+y=\sqrt{269}$$

$$\therefore\ $$ $$x^2-y^2=\left(x+y\right)\left(x-y\right)=\left(\sqrt{269}\right)\left(13\right)=13\sqrt{269}$$

Hence, the correct answer is Option C