Multiple regression - how to estimate β3 algebraically?

[sandrine]

Following Gujarati Basic Econometrics book, we can see on chapter about Multiple Regression 7.4. the equations of β1, β2 and β3 using Ordinary Least Squares method. The book doens't show the proof of β2 (but can be easily found on internet). I need to know how to get to β3 formula algebraically, because I already found some information about how to do using matrix.

Thank you, I need this demonstration step by step as soon as possible, for next week.