Need help with a simplification question

[i-love-physics]

Homework Statement

*refer to attached drawing*

Homework Equations

*refer to attached drawing*

The Attempt at a Solution

Basically i don't understand how (x+4) exponent of 3 disappeared in the simplfication.

My attempts at solution were trying to expand the brackets and seeing if i could figure it out that way but i still couldn't.


Could someone please look at the attached picture and explain to me how that simplication occured. Or if you can not do that could you please tell me which chapters of my book i must read in order to understand it (my book covers all chapters of mathematics, so just tell me the relevant mathemathic topics please)

Greatly appreciated if someone could help us out.

 

[VietDao29]

They factor (x + 4)² out. Have you covered this:
ab + ac = a(b + c)?
If so, it goes like this:
$$\frac{3(x - 3) (x + 4) ^ 2 - 2 (x + 4) ^ 3}{(x - 3) ^ 3}$$
$$= \frac{3(x - 3) (x + 4) ^ 2 - 2 (x + 4) ^ 2 (x + 4)}{(x - 3) ^ 3}$$
Now, we pull out the factor (x + 4)², and arrive at:
$$= \frac{(x + 4) ^ 2 \left[ 3(x - 3) - 2 (x + 4) \right]}{(x - 3) ^ 3}$$
Can you get it? :)

 

[i-love-physics]

thanks

thank you so much vietdao
I can't believe the answer was so simple yet i was unable to see it
You have cleared up my brain vietdao
I have never factored numbers inside brackets before that's probably what my problem was.

Anyway, thanks mate!.