Simplify if you can i couldn't?

Question

x-8 all over xsquared -4x+4 multiplied by 3xsquared +6x+12 all over xsquared -4x+4

Answer 1

As I understand the problem, you mean:

x - 8 3x² + 6x + 12
-------------- * -------------------
x² - 4x + 4 x² - 4x + 4

This can be made smaller by combining the demominators and reducing the polynomials to simplier forms:

(x - 8) (3x² + 6x + 12)
-------------------------------
(x² - 4x + 4) (x² - 4x + 4)

(x - 8) (3x² + 6x + 12)
-------------------------------
(x - 2)² (x - 2)²

(x - 8) (3x² + 6x + 12)
-------------------------------
(x - 2)^4 note: "^4" just means to the 4th power


3 (x - 8) (x² + 2x + 4)
-------------------------------
(x - 2)^4


I think that is about as simply as one would go. The (x² + 2x + 4)
term could be simplified some more, but it would make the overall equation more complex.

Hope this helps. If this wasn't the problem, please let me know what I didn't understand and I will try again.

Answer 2

Ok, your equation is written like this:
(x - 8)/(x² - 4x + 4) * (3x² + 6x + 12)/(x² - 4x + 4)

Now, since multiplication and division distribute, the equation can be written:
(x - 8)(3x² + 6x + 12) / (x² - 4x + 4)²

Factor the terms:
3(x - 8)(x² + 2x + 4) / (x - 2)^4

This is in most simplified form - unless you want to factor the quadratic using complex numbers, in which case you get:
3(x - 8)(x + 1 + i sqrt3)(x + 1 - i sqrt3) / (x - 2)^4