The convolution of two heaviside distributions from $$D'(\mathbb{R}^2)$$ is given to be
$$ H(t-|x|)*H(t-|x|)=H(t-|x|)(t^2-x^2)/2$$
Writing out the definition using integrals isn't really helping to get the $$(t^2-x^2)/2$$ term.
How can this possibly be done?