TITLE: How should I prove $(a+b)^3= a^3+3ab(a+b)+b^3$ --- Model or figure?
QUESTION [7 upvotes]: In what way can I prove/verify $(a+b)^3= a^3+3ab(a+b)+b^3$ ? Should I make a 3D model, or create 2D figure? In the case of 3D model, I have made $a^3$ and $b^3$; i.e cube'a' and cube'b'. I don't know what to do with $3a^2b+ 3b^2a$, in case I'm making a model. Previously, I made a figure by cutting paper pieces to verify $(a+b+c)^2$. I want to know whether model can be made or not. If not, then how must I prove $(a+b)^3=a^3+3ab(a+b)+b^3$ ?

REPLY [17 votes]: $\phantom{Body must be at least 30 characters; you entered 0.}$