Question

How do you factor this polynomial expression?

Answer 1

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.

Answer 2

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