Problems with covariance and correlation matrices in college probability and mathematical statistics

Using the bilinear character of the Cov operation (the nature of the covariance) one gets:

cov(X+2Y,2X-Y)=cov(X,2X)+cov(2Y,2X)-cov(X,Y)-cov(2Y,Y)

=2cov(X,X)+4cov(X,Y)-cov(X,Y)- 2cov(Y,Y)

=2DX+3cov(X,Y)-2DY