Regression: centered vs. uncentered predictors [duplicate]

I'm trying to understand how/why centering predictors in a 2 predictor regression model would change the coefficients

Lets say I have 2 centered predictors and an interaction term, predicting a continuous Y variable that is not centered, and I have gone through the process of calculating all the regression coefficients (b0-3).

Now, the question is, if I were to uncenter the 2 predictors, how would the coefficients change (if at all)?

From my understanding, the distribution of data points would not change, nor would the regression plane. However, by centering/uncentering we change the (X1, X2, Y) value of each datapoint. I don't believe this would change the b3 interaction coefficient because the relationship between the simple slopes would not be affected. The coefficients for the intercept and the 2 predictors, however, should change because we've essentially changed the scale for each of the predictors.

Can anyone shed some light on why/how this happens? and how do you determine the magnitude/direction of these changes?