How do you simplify this?

Question

zenmo · Answer

$$x(14-\frac{ x }{2 }-\frac{ \pi }{ 4 }x)+\frac{ \pi }{ 8 }x^2$$ to get $$14x-\frac{ 1 }{2}x^2-\frac{ \pi }{ 8}x^2$$?

directrix · Answer

http://openstudy.com/users/zenmo#/updates/5652f70ce4b0bdf21482cc64

zenmo · Answer

I closed the question, and opened a new one in-case I made the question confusing.

directrix · Answer

I went back and verified part A. The question is now direct.

My question to you is what happen to the pi term when you distributed the x?

If you would write out the complete distribution of x over the 3 terms in the parentheses, I think you will see the error.

zenmo · Answer

$$x(14-\frac{ x }{ 2 }-\frac{ \pi }{ 4 }x)+\frac{ \pi }{ 8 }x^2$$
= $$14x-\frac{ 1 }{ 2 }x^2-\frac{ \pi }{ 4 }x^2+\frac{ \pi }{ 8}x^2$$. I don't know how that would get the simplified version that I'm looking for.

ganeshie8 · Answer

Hint  : 

$$\dfrac{\pi}{4} = \dfrac{2\pi}{8}$$

ganeshie8 · Answer

$x(14-\frac{ x }{ 2 }-\frac{ \pi }{ 4 }x)+\frac{ \pi }{ 8 }x^2$

 $=14x-\frac{ 1 }{ 2 }x^2-\frac{ \pi }{ 4 }x^2+\frac{ \pi }{ 8}x^2$

 $=14x-\frac{ 1 }{ 2 }x^2-\frac{ 2\pi }{ 8 }x^2+\frac{ \pi }{ 8}x^2$

ganeshie8 · Answer

now combine the last two terms

zenmo · Answer

Ah, I see it now. $$-\frac{ 2\pi }{ 8 }x^2+\frac{ \pi }{ 8 }x^2= -\frac{ 2\pi }{ 8 }+\frac{ 1\pi }{ 8}=-\frac{ \pi }{  }$$

zenmo · Answer

-pi/8

ganeshie8 · Answer

who ate x^2

zenmo · Answer

yea -(pi/8)x^2 **

zenmo · Answer

I was looking at a practice-version solution example, and I didn't know how they simplified this part. Thanks! :) Other then that, I understand on how to do the rest of the problem. Just needed a little refresh on simplication.