Math Expansion Explanation

[CincyAndroiDeveloper]

I'm having trouble understanding how you expanded the following equation:(A+tb−C)⋅(A+tb−C)=r2
to the final form:
t2b⋅b+2tb⋅(A−C)+(A−C)⋅(A−C)−r2=0
When trying myself, I ended up with the following equation:
A^2-2AC+t^2b^2+2Atb-2tbC+C^2
which is significantly different from what you derived. Could you provide any insight into where I went wrong with the equation above?

[trevordblack]

(A+tb−C)⋅(A+tb−C)=r_2
(tb + (A-C))⋅(tb + (A-C)) = r_2
(tb)⋅(tb) + 2*tb⋅(A-C) + (A-C)⋅(A-C) = r_2
t^2b⋅b+ 2*tb⋅(A-C) + (A-C)⋅(A-C) - r_2 = 0

[CincyAndroiDeveloper]

Thank you for such a quick response. The explanation was exactly what I was missing.