Here is another more direct proof so that you can check the prob

Suppose

x=(a+b)^2+2*a*b,

y=(c+d)^2+2*c*d,

then after some simple calculation, one can check that

xy=(u+v)^2+2*u*v,

whereu=a*c+b*d and v=a*d+b*c+4*b*d.

In your example, F(-13,2)=69.