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## #1 2014-05-15 01:27:27

mittalanirudh.17
Member
Registered: 2014-05-15
Posts: 4

### Need Urgent Help!!

Can anyone explain me how to solve the following problem

Factorise -  x^12 - y^12

Would be really obliged

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## #2 2014-05-15 01:29:00

bobbym
From: Bumpkinland
Registered: 2009-04-12
Posts: 89,150

### Re: Need Urgent Help!!

Hi;

Is that a minus in front of the x^12?

In mathematics, you don't understand things. You just get used to them.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

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## #3 2014-05-15 01:33:55

ShivamS
Member
Registered: 2011-02-07
Posts: 3,612

### Re: Need Urgent Help!!

If you mean to factor -x^12-y^12 , it is

If you mean to factor x^12-y^12, it is

Last edited by ShivamS (2014-05-15 01:35:22)

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## #4 2014-05-15 01:36:06

bobbym
From: Bumpkinland
Registered: 2009-04-12
Posts: 89,150

### Re: Need Urgent Help!!

That is what I mean. The first one maybe can be done by pen and paper but the second one needs a CAS.

In mathematics, you don't understand things. You just get used to them.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

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## #5 2014-05-15 01:37:58

ShivamS
Member
Registered: 2011-02-07
Posts: 3,612

### Re: Need Urgent Help!!

I don't want to do even the first one without a CAS.

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## #6 2014-05-15 01:40:26

bobbym
From: Bumpkinland
Registered: 2009-04-12
Posts: 89,150

### Re: Need Urgent Help!!

I agree. That is no picnic.

In mathematics, you don't understand things. You just get used to them.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

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## #7 2014-05-15 01:43:12

Agnishom
Real Member
From: The Complex Plane
Registered: 2011-01-29
Posts: 18,223
Website

### Re: Need Urgent Help!!

Here is how:
x^12 - y^12
= (x^6)^2 - (y^6)^2
= (x^6 + y^6)(x^6 - y^6)
= ((x^2)^3 + (y^2)^3)((x^3)^2 - (y^3)^2)
= ((x^2)^3 + (y^2)^3)(x^3 + y^3) (x^3 - y^3)
= (x^2 + y^2) (x^4 - x^2 y^2 + y^4)(x + y) (x^2 - x y + y^2)(x - y) (x^2 + x y + y^2)

We are using a few  identities here:

Last edited by Agnishom (2014-05-15 01:56:50)

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
'You have made another human being happy. There is no greater accomplishment.' -bobbym

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## #8 2014-05-15 01:44:18

ShivamS
Member
Registered: 2011-02-07
Posts: 3,612

### Re: Need Urgent Help!!

You can use sum of cubes formula for the first one.

Agnishom wrote:

@bobbym, it is not.

Here is how:
x^12 - y^12 = (x^6)^2 - (y^6)^2 = (x^6 + y^6)(x^6 - y^6) = ((x^2)^3 + (y^2)^3)((x^3)^2 - (y^3)^2) = ((x^2)^3 + (y^2)^3)(x^3 + y^3) (x^3 - y^3) = (x^2 + y^2) (x^4 - x^2 y^2 + y^4)(x + y) (x^2 - x y + y^2)(x - y) (x^2 + x y + y^2)

But a CAS did that for you. Of course it is possible to do by hand but will take a long time.

Last edited by ShivamS (2014-05-15 01:45:03)

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## #9 2014-05-15 01:45:23

bobbym
From: Bumpkinland
Registered: 2009-04-12
Posts: 89,150

### Re: Need Urgent Help!!

That is algebraically correct!

In mathematics, you don't understand things. You just get used to them.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

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## #10 2014-05-15 01:46:42

Agnishom
Real Member
From: The Complex Plane
Registered: 2011-01-29
Posts: 18,223
Website

### Re: Need Urgent Help!!

Please do not confuse the newbie. I agree that it is tedious but this kind of questions are asked in Middle School and you are considered a dummy if you do not answer them.

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
'You have made another human being happy. There is no greater accomplishment.' -bobbym

Online

## #11 2014-05-15 01:48:13

ShivamS
Member
Registered: 2011-02-07
Posts: 3,612

### Re: Need Urgent Help!!

Agnishom wrote:

Please do not confuse the newbie. I agree that it is tedious but this kind of questions are asked in Middle School and you are considered a dummy if you do not answer them.

Please tell me which Middle School.

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## #12 2014-05-15 01:50:05

bobbym
From: Bumpkinland
Registered: 2009-04-12
Posts: 89,150

### Re: Need Urgent Help!!

in Middle School and you are considered a dummy if you do not answer them

In mathematics, you don't understand things. You just get used to them.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

Offline

## #13 2014-05-15 01:52:53

Agnishom
Real Member
From: The Complex Plane
Registered: 2011-01-29
Posts: 18,223
Website

### Re: Need Urgent Help!!

In the seventh and eighth grade, they can ask you to do this by hand.

But a CAS did that for you. Of course it is possible to do by hand but will take a long time.

I really did it by hand so that the OP gets how to do it.

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
'You have made another human being happy. There is no greater accomplishment.' -bobbym

Online

## #14 2014-05-15 01:54:26

bobbym
From: Bumpkinland
Registered: 2009-04-12
Posts: 89,150

### Re: Need Urgent Help!!

Okay, that is a very nice solution then. I did not see that.

In mathematics, you don't understand things. You just get used to them.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

Offline

## #15 2014-05-15 01:55:02

ShivamS
Member
Registered: 2011-02-07
Posts: 3,612

### Re: Need Urgent Help!!

Well, not here in the US or Canada.

But even in India, there is little thinking involved in doing this question by hand. It is just a rote computation problem, which is a waste of one's time.

I don't know how you did it in one minute

Last edited by ShivamS (2014-05-15 01:55:51)

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## #16 2014-05-15 01:59:18

Agnishom
Real Member
From: The Complex Plane
Registered: 2011-01-29
Posts: 18,223
Website

### Re: Need Urgent Help!!

Thank you, bobbym.

Well, in the begining, in order to see if you can actually recognise those patterns or not, these problems are given to you.

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
'You have made another human being happy. There is no greater accomplishment.' -bobbym

Online

## #17 2014-05-15 02:01:38

bobbym
From: Bumpkinland
Registered: 2009-04-12
Posts: 89,150

### Re: Need Urgent Help!!

Interesting to see what different places put emphasis on.

In mathematics, you don't understand things. You just get used to them.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

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## #18 2014-05-15 02:04:49

Agnishom
Real Member
From: The Complex Plane
Registered: 2011-01-29
Posts: 18,223
Website

### Re: Need Urgent Help!!

But being able to recognise where a^3 - b^3 and a^2 - b^2 occurs is important.

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
'You have made another human being happy. There is no greater accomplishment.' -bobbym

Online

## #19 2014-05-15 02:07:22

bobbym
From: Bumpkinland
Registered: 2009-04-12
Posts: 89,150

### Re: Need Urgent Help!!

It gets used in problems.

In mathematics, you don't understand things. You just get used to them.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

Offline

## #20 2014-05-15 02:08:42

Agnishom
Real Member
From: The Complex Plane
Registered: 2011-01-29
Posts: 18,223
Website

### Re: Need Urgent Help!!

That is why it is important. Is it not?

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
'You have made another human being happy. There is no greater accomplishment.' -bobbym

Online

## #21 2014-05-15 02:10:45

bobbym
From: Bumpkinland
Registered: 2009-04-12
Posts: 89,150

### Re: Need Urgent Help!!

It is good that you are so proficient with this type of problem. But as you know I would have turned to the heavy machinery after about a minute...

In mathematics, you don't understand things. You just get used to them.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

Offline

## #22 2014-05-15 03:53:33

mittalanirudh.17
Member
Registered: 2014-05-15
Posts: 4

### Re: Need Urgent Help!!

Thank you very much, btw all of you are Indians

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## #23 2014-05-15 05:24:23

bobbym
From: Bumpkinland
Registered: 2009-04-12
Posts: 89,150

### Re: Need Urgent Help!!

2 out of 3 ain't bad.

In mathematics, you don't understand things. You just get used to them.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

Offline

## #24 2014-05-15 05:47:46

Agnishom
Real Member
From: The Complex Plane
Registered: 2011-01-29
Posts: 18,223
Website

### Re: Need Urgent Help!!

I think 3 out of 4

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
'You have made another human being happy. There is no greater accomplishment.' -bobbym

Online

## #25 2014-05-15 05:49:28

bobbym
From: Bumpkinland
Registered: 2009-04-12
Posts: 89,150

### Re: Need Urgent Help!!

Counting him, yes.

In mathematics, you don't understand things. You just get used to them.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

Offline