Need help to factorize.

Farzin

Junior Member
Joined
Mar 13, 2017
Messages
77
Hi,
I have been stuck on factorizing this: \(\displaystyle a^2-2ab+a^2b-2b^2\).
I thought I could solve it by making \(\displaystyle (a+b)\) as one factor but it didn't work then I tried to add and deduct some terms which that didn't lead me to anything either.
I don't really know how what to next.
Any help would be greatly appreciated.
 

Dr.Peterson

Elite Member
Joined
Nov 12, 2017
Messages
8,305
I'm wondering if you might have copied something wrong. With three terms of degree 2 and one of degree 3, it seems like it might not factor, though I can't be sure. One small change would make it easy.
 

Farzin

Junior Member
Joined
Mar 13, 2017
Messages
77
I'm wondering if you might have copied something wrong. With three terms of degree 2 and one of degree 3, it seems like it might not factor, though I can't be sure. One small change would make it easy.
No everything is correct. I know it could be much easier with a small change. :)
 

HallsofIvy

Elite Member
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Jan 27, 2012
Messages
6,402
I would be inclined to write \(\displaystyle a^2+ 2ab+ a^2b- 2b^2\) as \(\displaystyle a^2+ 2ab+ b^2+ a^2b- 3b^2= (a+ b)^2+ a^2b- 3b^2= (a+ b)^2+ b(a^2- 3b)\).

That's about the best you can do.
 

Dr.Peterson

Elite Member
Joined
Nov 12, 2017
Messages
8,305
That's about all I could do, too. But when I set the expression to 0 and graph it, it seems clear that it is the product of two expressions that don't look like polynomials, which is very intriguing. I haven't figured out what they are.

1596204793852.png

@Farzin, where did this come from?
 

Farzin

Junior Member
Joined
Mar 13, 2017
Messages
77
That's about all I could do, too. But when I set the expression to 0 and graph it, it seems clear that it is the product of two expressions that don't look like polynomials, which is very intriguing. I haven't figured out what they are.

View attachment 20735

@Farzin, where did this come from?
Thanks for your attempts, this was given to me by a friend and we both are working on it.
 

Otis

Elite Member
Joined
Apr 22, 2015
Messages
2,537
… write \(\displaystyle a^2\) \(\displaystyle +\) \(\displaystyle 2ab+ a^2b- 2b^2\) …

\(\displaystyle (a+ b)^2+ b(a^2- 3b)\)
The term 2ab should be subtracted, making the result

\(\displaystyle (a - b)^2 \,+\, b\hspace{.09em}(a^2 - 3b)\) …

\(\;\)
 
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