Expected value of random variables - On average, how many points do you expect to receive in each round of this game?

Let $(x,y)$ be the outcome of the random experiment ($x$ represents the outcome of the blue die and $y$ represents the outcome of the red die), for which you will receive \[f(x,y)= 8x^2-9y^2.\] Expectation of the number of points is \[E(f(x,y))=\sum_{1\leq x, y \leq 6} f(x,y)p(x,y)=\sum_{1\leq x, y \leq 6} (8x^2-9y^2 ) \frac{1}{36}\] \[=\frac{1}{36}\sum_{1\leq x, y \leq 6} 8x^2 -\frac{1}{36}\sum_{1\leq x, y \leq 6} 9y^2 \] \[=\frac{8}{36}\sum_{x=1}^{6}\sum_{y=1}^{6}x^2-\frac{9}{36}\sum_{x=1}^{6}\sum_{y=1}^{6}y^2\] \[=-\frac{1}{36}\sum_{x=1}^{6}\sum_{y=1}^{6}y^2=-\frac{6}{36}\sum_{y=1}^{6}y^2=-\frac{1}{6}(91)=-\frac{91}{6}.\]