How would you expand the double summation:

$\displaystyle \sum\limits_{i}^2{\sum\limits_{j}^2{y_{i}y_{j}a_{i j}}}$

I understand that:

$\displaystyle \sum\limits_{i}^2{\sum\limits_{j}^2{y_{i}y_{j}}}$

Gets you something like:

$\displaystyle

y_{1}^{2}+y_{12}+ y_{21}+y_{2}^{2}

$

and

$\displaystyle \sum\limits_{i}^2{\sum\limits_{j}^2{a_{ij}}}$

is

$\displaystyle

a_{11}+a_{12}+a_{21}+a_{22}

$

But how can you combine these two? Is it as simple as foiling the entire thing?