(a+b+c)² = a² + b² + c² + 2(ab + ac + bc)pic.twitter.com/dpzsmzoB1N
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I think the relationship is a little clearer with a diagonal alignment:pic.twitter.com/4Y3DRDyKf7
This is great to visualise, but proofs nothing. We need both, the symbolic algebraic understanding, and whenever possible, a visualization or example that gives the 'feeling' of the intended meaning.
One face of Montessori binomial cube use by childrens from 4 years :-) #KinestheticLearning and the same one in #legopic.twitter.com/y7SrermgOZ
It's not a proof : the calculation is easy and is THE proof. (a+b)²= (a+b) * (a+b) =a²+ab + ab+b² =a²+2ab+b² It's not more -or less- difficult it's just applying the algebric properties in an Abelian Group
And for a lot of people visualization helps understand what is going on.
Ah, voilà résumé mon savoir en maths.
C'est un bon début 
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