Factoring Polynomials

1. Feb 20, 2006

Hollysmoke

I am stuck on this one polynomail factoring problem and I was wondering if someone could help me with it:

16a^2 - 24ab + 9b^2 - 25c^2

I tried factoring the first 3 terms as a trinomial but I'm not sure if that's what I'm supposed to do. What I wrote down so far is:

(4a -5c)(4a +5c)

2. Feb 20, 2006

Hollysmoke

Note: There should be a space between the 5c and 4a

3. Feb 20, 2006

Tide

Hint: Express the first three terms as a perfect square then factor the difference between squares. :)

4. Feb 20, 2006

topsquark

$$(16a^2-24ab+9b^2)-25c^2$$
$$(4a-3b)^2-25c^2$$

Now note that this is in the form of the difference of two squares, i.e.
$$x^2-y^2 = (x+y)(x-y)$$ where x = 4a-3b and y = 5c. So finally:
$$(16a^2-24ab+9b^2)-25c^2 = (4a-3b+5c)(4a-3b-5c)$$.

(And, of course, always multiply it back out to check the answer.)

-Dan

5. Feb 21, 2006

konartist

and of course, after you find X, put it into the original problem to make sure your value works.

6. Feb 21, 2006

Tide

I think you should leave something for the OP to do! :)