My teacher gave us the answer to this problem but I am having trouble showing my work.

$
5m^3(m^3-1)^2-3m^5(m^3-1)^3
$

when i work it out step by step i get

$m^3(m^3-1)^2(5-3m^2(m^3-1))$
$m^3(m^3-1)^2(5-3m^5+3m)$
$m^3(m^3-1)^2(5-3m^5+3m)$

I pretty much get stuck right there... the answer i should get is:

$
m^3(m-1)^2(m^2+m+1)^2(5+3m^2-3m)^5$

If anyone can figure out how could you list the steps that come to the conclusion? I can deduct what is going on without grammatical explanation, I just need to see the steps.

2. the answer doesn't seem to be correct, the highest power of m in the answer is 19 while the highest power of m in the question is 16

your working is correct to where it is now but i just don't see how you are going to get the answer provided by your teacher

ugh, now i am really pissed. :/ i spent like an hour and a half trying to figure that problem out. worst part about it is that the back of the book has that solution listed also. I did notice thought that i typed one part incorrectly.

$m^3(m-1)^2(m^2+m+1)^2(5+3m^2-3m^5)$
rather than:

$m^3(m-1)^2(m^2+m+1)^2(5+3m^2-3m)^5$

do you see any way that this may make a difference?

4. Hello,

Originally Posted by Waffl3z

ugh, now i am really pissed. :/ i spent like an hour and a half trying to figure that problem out. worst part about it is that the back of the book has that solution listed also. I did notice thought that i typed one part incorrectly.

${\color{red} m^3(m-1)^2(m^2+m+1)^2(5+3m^2-3m^5)}$
rather than:

$m^3(m-1)^2(m^2+m+1)^2(5+3m^2-3m)^5$

do you see any way that this may make a difference?
Better !
Notice that the degree of the red thing is 3+2+4+5=14

Originally Posted by Waffl3z
My teacher gave us the answer to this problem but I am having trouble showing my work.

$
5m^3(m^3-1)^2-3m^5(m^3-1)^3
$
<< the degree is max(3+3, 5+9)=14 so it's ok

when i work it out step by step i get

$m^3(m^3-1)^2(5-3m^2(m^3-1))$
$m^3(m^3-1)^2(5-3m^5+3m^{\color{red}2})$ mistake
$m^3(m^3-1)^2(5-3m^5+3m)$

I pretty much get stuck right there... the answer i should get is:

$
m^3(m-1)^2(m^2+m+1)^2(5+3m^2-3m)^5$

If anyone can figure out how could you list the steps that come to the conclusion? I can deduct what is going on without grammatical explanation, I just need to see the steps.
I've pointed out in red the important things