y=a+b1x1+b2x2+b3x1x2+b4x3+other terms $

Let's say, I am only interested in coefficient b3. The magnitude of coefficient b3 is 0.54 and its t value is 4.50 and the magnitude of the coefficient b2 is 2.00 and it's t value is 3.00. Now after including the interaction term x2x3

y=a+b1x1+b2x2+b3x1x2+b4x3+b5x2x3+other terms $

, the magnitude of the coefficient b3 is 0.53 and t value is 4.30 and the magnitude of the coefficient b2 is 300 and t value is 0.001. Note that the coefficient b1 doesn't change much.

I would like to know whether I should consider adding the interaction term x2x3 . I want to reiterate that I am only interested in coefficient b3.