SOLUTION: Please factorize the following 15x2 -2x -1 and a3 +6a2b +12ab3 +8b3 thank you

Question 854423: Please factorize the following
15x2 -2x -1
and
a3 +6a2b +12ab3 +8b3
thank you
Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!

(I know you wrote , but I think there was a typo somewhere).

How did I get it?

The factorization of

is easier to calculate this way:
If <--> ,

If that is Greek to you, there is another, more traditional way.
To factorize something like , you multiply the coefficients at the ends
(in this case, 15 and -1, that multiply to give -15),
and look for pairs of factors of that result that will add to the middle coefficient (-2 in this case).
When you figure out that 3 and -5 are those factors,
you re-write the polynomial with two middle terms with those coefficients,
that is and in place of the middle term ,
and then you factorize by grouping:

With it is a question of realizing that
is the cube of and
is the cube of .
That should make you suspect that it could be the cube of a binomial:

If you do the indicated operations,
and ,
and you find that indeed
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