Get Quick Help with Factoring Homework - (x-1)y^2 + (1-x^2) Simplified

[Loppyfoot]

Homework Statement

Could someone help me factor,
((x-1)y^2)+(1-(x^2))

The Attempt at a Solution

Is it possible to get to:
(x-1)(y^2-x-1)?

 

[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.

 

[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)?

 

[fss]

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)?

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

 

[Loppyfoot]

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

 

[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)

 

[Loppyfoot]

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

 

[fss]

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

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

 

[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)?

 

[fss]

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

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

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.

Hint: you already know how the result needs to look. Use this to your advantage...

 

[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.