Here's a rule that I learned from my algebra teacher almost 60 years ago. It's so handy, and I use it so often, that it's still fresh in my mind, and even though it's so old, it still works !
In fact, it's so useful that it would be a great item for you to memorize and keep in your math tool-box.
==> To factor the difference of two squares, write
<em>(the sum of their square roots) </em>times<em> (the difference of their square roots)</em> .
That's exactly what you need to solve this problem. I'll show you how it works:
<u>9x² - 25</u>
You look at this for a few seconds, and you realize that 9x² is the square of 3x , and 25 is the square of 5 . So this expression is the difference of two squares, and you can use the shiny new tool I just handed you.
The square roots are 3x and 5 .
So the factored form of the polynomial is <em>(3x + 5) (3x - 5)</em> .
That's all there is to it. If you FOIL these factors out, you'll see that you wind up with the original polynomial in the question.
