This is Day 14 of 31 Days of Math Learning Success. Follow all the days here and check out others that are writing for 31 days here.

It’s a round ball and a round bat, and you got to hit it square.
~ Pete Rose

Today’s math learning success tip is short and sweet – write out your squares.

In all the errors I’ve seen by students (and me), this one takes the cake.

What Squaring Means

$latex 3^2$ means $latex 3 \times 3$.

Just like $latex 2^5$ means $latex 2 \times 2 \times 2 \times 2 \times 2$.

No biggie once you get your brain wrapped around it.

Except it’s very easy to do $latex 3^2$ in your head and accidentally do $latex 3 \times 2$.

So even though you CAN do it in your head, write it out. At least for the first few hundred times you have to do it.

Squaring Gone Wild

If you’re used to writing all those little squares and powers, this won’t bother you much.

But if you’ve already decided you can do it in your head, you might glitch yourself on this next one: $latex (x + y)^2$

If you’re a “cool student” you might want to quickly do this one in your head: $latex x^2 + y^2$

But that doesn’t work.

See it with some “regular” numbers:

$latex (7+5)^2$ is $latex 12^2$ or $latex 144$, right?

But is $latex 7^2 + 5^2$ also $latex 144$? Nope. It’s $latex 49 + 25$ or $latex 74$.

Stretch it!

If we write out $latex 3^2$, why not write out $latex (x+y)^2$?

Then it’s $latex (x+y)(x+y)$.

Aha!

You might jump into the aluminum wrap zone here (FOIL). And you’d be right!

$latex (x+y)(x+y)$ is $latex x^2 + 2xy + y^2$, a bit different from $latex x^2 + y^2$. Not much, but enough to make a difference.

And if you look at this with the $latex (7+5)^2$ example, that would work too. But I’ll let you mess with that one on your own. 🙂

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