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

Can anyone explain me how to solve the following problem

Factorise - x^12 - y^12

Would be really obliged

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 106,367

Hi;

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

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.****No great discovery was ever made without a bold guess. **

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**ShivamS****Member**- Registered: 2011-02-07
- Posts: 3,648

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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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 106,367

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.****If it ain't broke, fix it until it is.****No great discovery was ever made without a bold guess. **

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**ShivamS****Member**- Registered: 2011-02-07
- Posts: 3,648

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

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 106,367

I agree. That is no picnic.

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.****No great discovery was ever made without a bold guess. **

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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'

I'm not crazy, my mother had me tested.

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**ShivamS****Member**- Registered: 2011-02-07
- Posts: 3,648

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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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 106,367

That is algebraically correct!

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.****No great discovery was ever made without a bold guess. **

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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'

I'm not crazy, my mother had me tested.

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**ShivamS****Member**- Registered: 2011-02-07
- Posts: 3,648

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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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 106,367

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

Are you sure about that?

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.****No great discovery was ever made without a bold guess. **

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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'

I'm not crazy, my mother had me tested.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 106,367

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.****If it ain't broke, fix it until it is.****No great discovery was ever made without a bold guess. **

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**ShivamS****Member**- Registered: 2011-02-07
- Posts: 3,648

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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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.

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

I'm not crazy, my mother had me tested.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 106,367

Interesting to see what different places put emphasis on.

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.****No great discovery was ever made without a bold guess. **

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

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

I'm not crazy, my mother had me tested.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 106,367

It gets used in problems.

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.****No great discovery was ever made without a bold guess. **

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That is why it is important. Is it not?

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

I'm not crazy, my mother had me tested.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 106,367

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.****If it ain't broke, fix it until it is.****No great discovery was ever made without a bold guess. **

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

Thank you very much, btw all of you are Indians

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 106,367

2 out of 3 ain't bad.

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.****No great discovery was ever made without a bold guess. **

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I think 3 out of 4

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

I'm not crazy, my mother had me tested.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 106,367

Counting him, yes.

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.****No great discovery was ever made without a bold guess. **

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