# Find PDF of $(X-Y)^2$- uniform distribution.

Let $$X,Y \sim U[-1,1]$$. $$X$$ and $$Y$$ are independent.How to find pdf of $$Z=(X-Y)^2$$?

My idea:

$$P(Z \le t)=P((X-Y)^2 \le t)=P(-\sqrt{t}\le X-Y \le \sqrt{t})=P(X-Y \le \sqrt{t})-P(X-Y \le -\sqrt{t})=F_{X-Y}(\sqrt{t})-F_{X-Y}(-\sqrt{t})$$.

Is it necessary to count convolution?