I too was taught to parrot it back and, given my mathematical ability, a parrot would have been better at it.

Would it have killed my math teacher to have done this, oh, 35 years ago now? Perhaps he didn't know it either?

It works for (a+b)^3 also if you make a cube. After that you're stuck in hyperspace.

He just presented a geometric version of the equation that does, indeed, make sense. It's more important, however, to understand how to extend the equation as that leads to the simplification of all formulae:

(a+b)2 = (a+b)*(a+b)

You would then use the (associative?) principal:

(a+b)*(a+b) = (a*a)+(b*b)+(a*b)+(a*b)
= a2 + b2 + 2(a*b)

Or something like that. It's been years since I had to do that, but I would not have been able to use these methods to simplify other equations far more complex than this one if the teacher had just shown me how to count squares.

It's more than "counting squares". It shows a concrete relationship between the formula and reality. Those of us with a bit of a right-brain need this.

Really? I've never had trouble with math. I'm with Tom though,35 years ago this short video would have been helpful.

That cute little long-haired hippy man with the funny accent seems pretty proud of himself on that one ...

Sure, his illustrative technique works for (a+b)^2 and even (a+b)^3. However, it does not work for powers greater than three. In cases greater than three, that operational method you/we learned years ago still works where Mr. Long-Hair's method does not.

Any math teacher who DOESN'T show this to his students needs a serious ass-kickin'. Geometric intuition needs training, and is essential for lots of scientists and engineers.

Powers past the cube need not go into hyperspace, but do require a good half-hour explanation of Pascal's triangle, counting combinations, and the Binomial Theorem. All of which is readily accessible to any seventh-grader exposed to basic algebra.

I think that most of the troubles with math come from NOT being taught to read the formula as a sentence. And expand them rather than using the contracted form (a+b)2.