[R] interpretation for multiple regression

[Irene Mantzouni]

Dear all,
 
probably this is quite clear for most of you but for me it is a headache...
 
I am regressing response A against the continuous covariate B and the relationship is clearly quadratic. 
When I add a second covariate B, the relationship becomes linear for both B and C. 
So, I expect that the interaction of B:C should also be significant, which is not the case.
How do you interpret this??
 
Thank you!