Expert: Paul Klarreich - 5/9/2006

Question
Hi, I have a very simple question.  How do you factor something like:

9c^2 - 24cd + 16d^2  ?

Also, what about:

c^2d^2 - 10cd + 16


This is actually work that I was out of school for, and thus missed, but it's due tomorrow, so any help would be greatly appreciated!  THANK YOU!

Answer
Hi, brittyyyyyyyy,

[did your parents really give you that name, or did your keyboard get stuck?]
 
Subject:  factoring
Question:  Hi, I have a very simple question. How do you factor something like:

9c^2 - 24cd + 16d^2 ???

Things like this factor to :

(__c +- __d)(__c +- ___d)

If you just had:

9c^2 - 24c + 16

you wouldn't have any trouble, right?  [Well,....]

So temporarily write that and try to factor it:

9c^2 - 24c + 16 = (3c - 4)(3c - 4) = (3c - 4)^2

Now write the actual answer:

9c^2 - 24cd + 16d^2 = (3c - 4d)^2



Also, what about:

c^2d^2 - 10cd + 16

If there weren't any d's, it would be:

c^2 - 10c + 16 = (c - 2)(c - 8)

and you wouldn't have any trouble.  So the first terms have to be cd's:

c^2d^2 - 10c + 16 = (cd - 2)(cd - 8)