If $$x - y = 4$$ and $$x^3 - y^3 = 316, y > 0$$ then the value of $$x^4 - y^4$$ is:

$$x-y=4$$...........(1)

$$\left(x-y\right)^3=64$$

$$x^3-y^3-3xy\left(x-y\right)=64$$

$$316-3xy\left(4\right)=64$$

$$12xy=252$$

$$xy=21$$..........(2)

$$x-y=4$$

$$\left(x-y\right)^2=4^2$$

$$x^2+y^2-2xy=16$$

$$x^2+y^2-2\left(21\right)=16$$

$$x^2+y^2=58$$..........(3)

$$\left(x+y\right)^2=x^2+y^2+2xy$$

$$\left(x+y\right)^2=58+2\left(21\right)$$

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

$$x+y=10$$..........(4)

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

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

$$=\left(58\right)\left(10\right)\left(4\right)$$

$$=2320$$

Hence, the correct answer is Option B