SQUARING A 3–DIGIT NUMBER

In my last blog I talked about squaring a 2–digit number. I know that most

teachers, even Middle School, will not be interested in my last blog, however

why stop there. Let's look at squaring a 3–digit number.

Last time it was: (a + b)(a + b) = a² + 2ab + b²

This time we have: (a + b + c)(a + b + c) =

a² + ab + ac + ba + b² + bc + ca + cb + c² =

a² + 2ab + b² + 2bc + c² + 2ac

So, when we look a number like 426, we need to look at it as

400 + 20 + 6 = 426

Square it: (400 + 20 + 6)(400 + 20 + 6)

We only need to use our counting digits, 4, 2, 6, with the help

of our zero to answer our question.

a = 400, b = 20, and c = 6

Thus, 400² + 2(400)(20) + 20² + 2(20)(6) + 6² +

2(400)(6)

1. 400² = 160000

2. 2(400)(20) = 16000

3. 20² = 400

4. 2(20)(6) = 240

5. 6² = 36

6. 2(400)(6) = 4800

Grand total is 181476

You may not be able to do something like this in your head

without a great deal of practice, but what if the number you

were squaring had a zero in it, like 403, or 260.

In 403 the b value would be 0, and the only therms in the formula

you would need would be a², 2ac, and c²

400² = 160000

2(400)(3) = 2400

3² = 9 TOTAL = 162409

260² = 200² + 2(200)(60) + 60²

= 40000 + 24000 + 3600

TOTAL = 67600

These last two examples, with practice, you can do in you

head and will show you how to use zeros correctly

when multiplying. I find that these kinds of mental

practices improve the mind. These will work well as

warm–up problems in the morning, or at the beginning

of any Math class.