# Rewriting an equation.

• Mar 31st 2010, 06:02 PM
p75213
Rewriting an equation.
Could somebody explain how we get the 2nd equation from the 1st?
1) 3 (x − 3)^3 (x + 5)^2 − 3 (x + 5)^3 (x − 3)^2

2) 3 (x − 3)^2 (x + 5)^2 [(x − 3) − (x + 5)]
• Mar 31st 2010, 06:27 PM
Wilmer
Quote:

Originally Posted by p75213
1) 3(x − 3)^3 (x + 5)^2 − 3(x + 5)^3 (x − 3)^2

2) 3(x − 3)^2 (x + 5)^2 [(x − 3) − (x + 5)]

let a = x-3 and b = x+5
3a^3 b^2 - 3a^2 b^3
3a^2 b^2(a - b)
Kapish?
• Mar 31st 2010, 06:47 PM
p75213
Sorry. Still don't get it. Wouldn't 3a^2b^2(a-b) expand into 3a^3b^2-3a^2b^3. Seems like I am missing something here.
• Mar 31st 2010, 06:47 PM
djsnare
Quote:

Originally Posted by p75213
Could somebody explain how we get the 2nd equation from the 1st?
1) 3 (x − 3)^3 (x + 5)^2 − 3 (x + 5)^3 (x − 3)^2

2) 3 (x − 3)^2 (x + 5)^2 [(x − 3) − (x + 5)]

I think they just factored out a common term:

http://www.djsnare.ca/equation2.jpg
If you were to multiply it out, you should get back to the first expression.
• Mar 31st 2010, 07:00 PM
Wilmer
Quote:

Originally Posted by p75213
Wouldn't 3a^2b^2(a-b) expand into 3a^3b^2-3a^2b^3.

Yes. I made typo; now corrected. But still same idea...
• Mar 31st 2010, 07:01 PM
p75213
Yep - that's it. Many thanks.