Factor this polynomial expression? 9x^2 - 25

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

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.

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