Quadratic factorising

[pixel2metal]

Daft question feel like I should know this:
9x^2 - 4y^2
It factorises to (3x+2y)(3x-2y) but I'm not sure how to get there. Something to do with completing the square? which I've never been very good at..
Thanks!

 

[Otis]

(3x+2y)(3x-2y) ... Something to do with completing the square?

Hi p2m. No, it's just one of the special factoring patterns that you're expected to memorize. That one is called a "Difference of Squares", and the general pattern looks like this:

(a^2 - b^2) = (a + b)(a - b)

In your exercise, we recognize that the term 9x^2 is the square of 3x and the term 4y^2 is the square of 2y.

Therefore, the given expression is a difference of two squares. (Subtraction indicates a difference.)

In the factoring pattern, a=3x and b=2y.

Do you have a textbook? There are other special factoring patterns (sum of cubes, difference of cubes, but there is no pattern for a sum of squares in the Real number system).

 

[pixel2metal]

Fantastic thanks. Have heard of difference of two squares, just didn't realise it was one you had to recognise and memorise ?
I'll have a look at the others too. Thanks for you answer!

 

[Deleted member 4993]

there is no pattern for a sum of squares

You mean in "real" region?

 

[Otis]

didn't realise [that pattern] was one you had to recognise and memorise

Indeed it is, for those continuing beyond middle-school math. It comes up "all the time".

 

[Otis]

You mean in "real" region?

Astute, as always!

I will update my wording...

?