The steps in factoring polynomials.?

Question

In certain polynomials there are several approaches and only some lead to the correct answer. For example.144a^2-64b^2.
I would see that it is difference of squares and make it (12a-8b)(12a+8b) However it is not the right answer. Is there a order of things to look for when factoring polynomials. Like GCF first than difference of squares then square roots?

Answer 1

You're on the right path. It's just that after you
got

(12a-8b)(12a+8b)

you can take another 4 out of each term to get
prime factors,

4*(3a-2b)*4(3a+2b) =
16(3a-2b)(3a+2b)

Answer 2

16y^2-25 it incredibly is a distinction of two squares. Its a made of this form: (a+b)(a-b) Memorize it: a²-b² = (a+b)(a-b) for the duration of this occasion a² = 16y², so a=4y and b²=25, b=5 subsequently: 16y²-25 = (4y+5).(4y-5) the subsequent polynomial is a suitable sq. trinomial. it is, a three words polynomial it is a superb sq.. How am i able to comprehend it? Memorize it: (a+b)²=a² + 2.a.b + b² it incredibly is a sq. and theere are 3 words interior the marvelous. z² -20z +a hundred is of the form a² +2ab +b²? If z²=a², a hundred = b² and -20z =2ab, we are able to put in the sq. form. z²=a² implies z=a a hundred = b² implies b = 10 or -10 2ab = 2.z.10 or -2.z.10, can any certainly one of those be -20z? definite, the 2d is precisely the midsection term of our trinomial. So: z²-20z+a hundred = (z-10)² Is the final one incredibly y²-sixteen+sixty 4? shouldn't or not that is y²-16y+sixty 4? word that it incredibly is a suitable sq. trinomial. found out a and b that makes it to have a form (a-b)².

Answer 3

How is it not correct?

(12a-8b)(12a+8b) =
144a^2 + 96ab - 96ab - 64b^2 =
144a^2 - 64b^2

It is just a difference of squares, you got it.

Answer 4

Yes. You would then factor more, the answer being
(3a-2b)(3a+2b)(12a+8b) I hope this helps! ^.^