Math help: factoring

[ChaoZ]

2x(2x-1)^2 - 4(x^2-1)(2x-1)
--------------------------------
(2x-1)^4


Helping my sister, but it's been so long. Am I suppose to cancel the (2x-1) in the numerator with the denominator?

 

[Brigandier]

((2x(2x-1)-4(x-1)(x+1))
-----------------------------------
(2x-1)^3

 

[darkswordsman17]

You've got to pull (2x-1) out of the top first, then cancel it out?

 

[Ticky]

2x(2x-1)-4(x^2-1)
------------------------
(2x-1)^3


4x^2-2x-4x^2+4
-----------------------
(2x-1)^3


-2x-4
-----------
(2x-1)^3

 

[ChaoZ]

Originally posted by: Ticky
2x(2x-1)^2-4(x^2-1)
------------------------
(2x-1)^3


4x^2-2x-4x^2+4
-----------------------
(2x-1)^3


-2x-4
-----------
(2x-1)^3

What happened to that?

 

[Ticky]

Originally posted by: ChaoZ

Originally posted by: Ticky
2x(2x-1)^2-4(x^2-1)
------------------------
(2x-1)^3


4x^2-2x-4x^2+4
-----------------------
(2x-1)^3


-2x-4
-----------
(2x-1)^3

What happened to that?

????

 

[ChaoZ]

The ^2 from the numerator in the problem.

 

[So]

Originally posted by: Ticky
2x(2x-1)-4(x^2-1)
------------------------
(2x-1)^3


4x^2-2x-4x^2+4
-----------------------
(2x-1)^3


-2x-4
-----------
(2x-1)^3

I think you added a negative sign at the last step. I'm tired and slightly sick, so mebbye I'm crazy, but shouldn't that numerator be 4-2x (or in your notation -2x+4)?

 

[RedArmy]

Cancel out the (2x-1) since it's in everything. You're left with ((4x^2)-2x)-((4x^2)-4) on the top and just (2x-1)^3 on the bottom. The top turns into (4x^2)-2x-(4x^2)+4 which reduces to 4-2x since the (4x^2) terms cancel out. Therefore you're left with (4-2x) all over (2x-1)^3.

Use parentheses people! It's incredibly important, especially when you're dealing with terms like 4(x^2-1) as that could be perceived two very different ways

 

[GodlessAstronomer]

Originally posted by: So

Originally posted by: Ticky
2x(2x-1)-4(x^2-1)
------------------------
(2x-1)^3


4x^2-2x-4x^2+4
-----------------------
(2x-1)^3


-2x-4
-----------
(2x-1)^3

I think you added a negative sign at the last step. I'm tired and slightly sick, so mebbye I'm crazy, but shouldn't that numerator be 4-2x (or in your notation -2x+4)?

Yes.

 

[ChaoZ]

Originally posted by: RedArmy
Cancel out the (2x-1) since it's in everything. You're left with ((4x^2)-2x)-((4x^2)-4) on the top and just (2x-1)^3 on the bottom. The top turns into (4x^2)-2x-(4x^2)+4 which reduces to 4-2x since the (4x^2) terms cancel out. Therefore you're left with (4-2x) all over (2x-1)^3.

Use parentheses people! It's incredibly important, especially when you're dealing with terms like 4(x^2-1) as that could be perceived two very different ways

Thanks. Took me a while to do it that way.

 

[Ticky]

Originally posted by: GodlessAstronomer

Originally posted by: So

Originally posted by: Ticky
2x(2x-1)-4(x^2-1)
------------------------
(2x-1)^3


4x^2-2x-4x^2+4
-----------------------
(2x-1)^3


-2x-4
-----------
(2x-1)^3

I think you added a negative sign at the last step. I'm tired and slightly sick, so mebbye I'm crazy, but shouldn't that numerator be 4-2x (or in your notation -2x+4)?

Yes.

Whoops.

 

[Born2bwire]

Originally posted by: Ticky

Originally posted by: GodlessAstronomer

Originally posted by: So

Originally posted by: Ticky
2x(2x-1)-4(x^2-1)
------------------------
(2x-1)^3


4x^2-2x-4x^2+4
-----------------------
(2x-1)^3


-2x-4
-----------
(2x-1)^3

I think you added a negative sign at the last step. I'm tired and slightly sick, so mebbye I'm crazy, but shouldn't that numerator be 4-2x (or in your notation -2x+4)?

Yes.

Whoops.

I hate leading negative signs. It should be:

2x-4
-----------
(1-2x)^3

 

[sao123]

nvmd.

 

[So]

Originally posted by: Born2bwire

Originally posted by: Ticky

Originally posted by: GodlessAstronomer

Originally posted by: So

Originally posted by: Ticky
2x(2x-1)-4(x^2-1)
------------------------
(2x-1)^3


4x^2-2x-4x^2+4
-----------------------
(2x-1)^3


-2x-4
-----------
(2x-1)^3

I think you added a negative sign at the last step. I'm tired and slightly sick, so mebbye I'm crazy, but shouldn't that numerator be 4-2x (or in your notation -2x+4)?

Yes.

Whoops.

I hate leading negative signs. It should be:

2x-4
-----------
(1-2x)^3

lol, we're doing great in this thread.

4-2x.

 

[Born2bwire]

Originally posted by: So

Originally posted by: Born2bwire

Originally posted by: Ticky

Originally posted by: GodlessAstronomer

Originally posted by: So

Originally posted by: Ticky
2x(2x-1)-4(x^2-1)
------------------------
(2x-1)^3


4x^2-2x-4x^2+4
-----------------------
(2x-1)^3


-2x-4
-----------
(2x-1)^3

I think you added a negative sign at the last step. I'm tired and slightly sick, so mebbye I'm crazy, but shouldn't that numerator be 4-2x (or in your notation -2x+4)?

Yes.

Whoops.

I hate leading negative signs. It should be:

2x-4
-----------
(1-2x)^3

lol, we're doing great in this thread.

4-2x.

The denominator.