\( 9{ x }^{ 2 }-25\\ \\ ={ 3 }^{ 2 }{ x }^{ 2 }-{ 5 }^{ 2 }\\ \\ ={ \left( 3x \right) }^{ 2 }-{ 5 }^{ 2 }\\ \\ =\left( 3x+5 \right) \left( 3x-5 \right) \)

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

** (the sum of their square roots) **times

**.**

*(the difference of their square roots)*That’s exactly what you need to solve this problem.

I’ll show you how it works:

**9x² - 25**

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

**.**

*(3x + 5) (3x - 5)*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.

I really think Sean is going to need an explanation of why you did what you did. The jump from the 3rd line to the 4th line is not obvious.