Help expanding this summation for VDW mixing rules

Question

I've hit a bit of a wall when trying to expand this summation but for the life of me can't get it right.

$\sum_{i} \sum_{j} y_i y_j {a_i}_j $

for a 2 component system.

Answer 1

For anyone that also struggles with it the answer is

y1y1a11 + y1y2a12 + y2y1a21 + y2y2a22

and noting a12 = a21 (for these specific mixing rules)

= (y1^2)a11 + 2y1y2a12 + (y2^2)a22