# How to simplify

1. Oct 27, 2013

### Elpinetos

I am currently stumped with a mental blackout, how do you simplify this again?

(-192x^2(4x-3)-4(27-64x^3))/(4x-3)^2

Wolfram Alpha spits out -32x-12, but how do you get there? :(

2. Oct 27, 2013

### rock.freak667

Expand out each bracket first and then simplify the terms with x's in them.

2(x+1) = 2x+2

x^3 +x^2 +2x^3 + 2x^2 = 3x^3 + 3x^2

After doing that, try to factor out (4x-3)

3. Oct 27, 2013

### Elpinetos

Now I have (-512x^3-576x^2-108)/(16x^2-24x+9), but how do I proceed?
I don't see how I can factor out (4x-3) out of this :/

4. Oct 27, 2013

### hops1

Hi, try using synthetic or long division

5. Oct 27, 2013

### Elpinetos

There must be an easier way, right? Oo

Since I got this from having to find the derivative of y=(27-64x^3)/(4x-3) and this is one of the basic problems in my text book. I'm quite sure it doesn't involve long division oO

6. Oct 27, 2013

### SteamKing

Staff Emeritus
Well, you are the one that wanted to know how WA got its answer.

I think if you re-examine the numerator in you original expression, the term (27 - 64x^3) is the difference of two cubes. If you break this term into its factors, and then check for cancellations, it might be easier than expanding everything at first.

7. Oct 28, 2013

### Elpinetos

Got it, thank you...
Fresh day, fresh mind

So simply make a polynomial devision BEFORE deriving... But how can I know that beforehand? :/

8. Oct 28, 2013

### SteamKing

Staff Emeritus
That's what the experience of doing a lot of math problems gives you.