How do I derive the poisson distribution?
$\displaystyle Cov(D+E, D-2E)=E( [(D+E)-(\overline{D}+\overline{E})][(D-2E)-(\overline{D}-2\overline{E})]$
Now expand the expression inside the expectation on the right hand side. Then use linearity of the expectation operator to express the right hand side as a sum of expectations, and use the fact that the means and variances of all the RV's are known and that they are independent to expand the resulting expression.
CB