Homework Help: Quick Factoring Help

1. Sep 28, 2010

Loppyfoot

1. The problem statement, all variables and given/known data
Could someone help me factor,
((x-1)y^2)+(1-(x^2))

3. The attempt at a solution
Is it possible to get to:
(x-1)(y^2-x-1)?

2. Sep 28, 2010

fss

Yes, it is possible to get there.

Work with the left-hand term; 1-x2. When you factor that, things should start looking more manageable.

3. Sep 28, 2010

Loppyfoot

So I get (x-1)y^2 + (1-x)(1-x)

Where do I go from there in order to factor out the (x-1)?

4. Sep 28, 2010

fss

What happens if you take out a -1 from one of the terms on the right?

5. Sep 28, 2010

Loppyfoot

Oh so, I got (x-1)y^2 - (x+1)(x-1) COrrect?

Last edited: Sep 28, 2010
6. Sep 28, 2010

fss

You can take out -1 from just the right-hand term.

(x-1)y^2 + (1-x)(1-x) = (x-1)y^2 + (-1) (?????) (1-x)

7. Sep 28, 2010

Loppyfoot

Ok, so I got: (x-1)y^2 - (x+1)(x-1)

8. Sep 28, 2010

fss

Incorrect. Look at the bolded term again. You're only taking -1 out of one quantity in the parentheses.

9. Sep 28, 2010

Loppyfoot

Oh, so would it be:
(x-1)y^2 - (-x-1)(x-1)?

But how do I get to:
(x-1)(y^2-x-1)?

10. Sep 28, 2010

fss

Oops, sorry, in post #3 you made an error which I didn't notice initially.

You need to factor this correctly for it to make any sense. Once you have it factored correctly and you take out a (-1) from one of the terms in the parentheses, you should be able to then rearrange the expression into something that resembles what you're trying to show.

11. Sep 29, 2010

Mentallic

All you really need are these 3 rules:

$$a^2-b^2=(a-b)(a+b)$$

$$ab=-(-a)(b)=-(a)(-b)$$

$$ab+ac=a(b+c)$$

Notice the first difference of two squares, as fss has pointed out you have made a mistake in factoring the 1-x2, so fix that first before moving on.