Does (x + y)^2 = x^2 + y^2

In a few projects that we’ve done over the last couple of days my younger son has gotten a little confused on some basic algebra. Not something I’m worried about as ideas like does:

(i) , or

(ii)

(in case that latex isn’t displaying properly, the entire expression is supposed to be under the square root.)

are questions that confuse everyone when learning algebra.

Today we did a short project to talk about these equations. We ended up spending most of the time on (i) just because it was a little easier to talk about. First, though, was just a quick look at both equations:

Now we looked at more carefully. You can see my younger son’s confusion at the beginning. To help get past that confusion we looked at what actually means.

As we were talking during the last project I noticed a bunch of snap cubes near by (from one of last week’s projects). Rather than move on to the square root example I thought it would be better (and also fun) to view the square example from a geometric perspective.

This was a fun discussion and I especially enjoyed seeing the boys find a few different geometric approaches to the problem.