Factoring special cases of polynomials

[Audentes]

I can't find any common factor for these:

9w^2 -16
4x^2 -4x +1
16n^2 -56n +49

what should i do?
Thanks
flo

 

[BenF77]

First one is a difference of squares. Next two are perfect square trinomials. None have a GCF.

 

[Dr.Peterson]

I can't find any common factor for these:

9w^2 -16
4x^2 -4x +1
16n^2 -56n +49

what should i do?
Thanks
flo

The next step after looking for a common factor of the terms is to use one of the "special cases" they mention in your title. What are they?

You should see a difference of squares and two "perfect square trinomials".

The latter doesn't really require using a special method; you can just factor as you would any trinomial. But it can be a little easier if you recognize that the first and last terms are squares, so maybe it has the form (a + b)^2. Determine what a and b have to be, and try it out!

 

[Audentes]

The next step after looking for a common factor of the terms is to use one of the "special cases" they mention in your title. What are they?

You should see a difference of squares and two "perfect square trinomials".

The latter doesn't really require using a special method; you can just factor as you would any trinomial. But it can be a little easier if you recognize that the first and last terms are squares, so maybe it has the form (a + b)^2. Determine what a and b have to be, and try it out!

So 9w² is 3w in each set of parentheses, and -16 becomes +4 and -4?

 

[BenF77]

So 9w² is 3w in each set of parentheses, and -16 becomes +4 and -4?

yes (3w+4)(3w-4)

 

[JeffM]

So 9w² is 3w in each set of parentheses, and -16 becomes +4 and -4?

Yes, you really should just memorize these special cases

[MATH]a^2 - b^2 = (a - b)(a + b);\ \text { and } p^2 \pm 2pq + q^2 = (p \pm q)^2.[/MATH]

 

[Audentes]

Yes, you really should just memorize these special cases

[MATH]a^2 - b^2 = (a - b)(a + b);\ \text { and } p^2 \pm 2pq + q^2 = (p \pm q)^2.[/MATH]

Ok thank you