Need help to factorize.

Farzin

Junior Member
Joined
Mar 13, 2017
Messages
80
Hi,
I have been stuck on factorizing this: [MATH]a^2-2ab+a^2b-2b^2[/MATH].
I thought I could solve it by making [MATH](a+b)[/MATH] 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.
 
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.
 
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. :)
 
I would be inclined to write a2+2ab+a2b2b2\displaystyle a^2+ 2ab+ a^2b- 2b^2 as a2+2ab+b2+a2b3b2=(a+b)2+a2b3b2=(a+b)2+b(a23b)\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.
 
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?
 
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.
 
… write a2\displaystyle a^2 +\displaystyle + 2ab+a2b2b2\displaystyle 2ab+ a^2b- 2b^2

(a+b)2+b(a23b)\displaystyle (a+ b)^2+ b(a^2- 3b)
The term 2ab should be subtracted, making the result

(ab)2+b(a23b)\displaystyle (a - b)^2 \,+\, b\hspace{.09em}(a^2 - 3b)

  \;
 
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