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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?

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