Math Is Fun Forum
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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
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
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.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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#3 2014-05-15 01:33:55
- ShivamS
- Member
- Registered: 2011-02-07
- Posts: 3,648
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
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
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.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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#5 2014-05-15 01:37:58
- ShivamS
- Member
- Registered: 2011-02-07
- Posts: 3,648
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
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: Need Urgent Help!!
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.
Always satisfy the Prime Directive of getting the right answer above all else.
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#7 2014-05-15 01:43:12
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'
I'm not crazy, my mother had me tested.
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#8 2014-05-15 01:44:18
- ShivamS
- Member
- Registered: 2011-02-07
- Posts: 3,648
Re: Need Urgent Help!!
You can use sum of cubes formula for the first one.
@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
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: Need Urgent Help!!
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.
Always satisfy the Prime Directive of getting the right answer above all else.
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#10 2014-05-15 01:46:42
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'
I'm not crazy, my mother had me tested.
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#11 2014-05-15 01:48:13
- ShivamS
- Member
- Registered: 2011-02-07
- Posts: 3,648
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.
Please tell me which Middle School.
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#12 2014-05-15 01:50:05
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: Need Urgent Help!!
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.
Always satisfy the Prime Directive of getting the right answer above all else.
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#13 2014-05-15 01:52:53
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'
I'm not crazy, my mother had me tested.
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#14 2014-05-15 01:54:26
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
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.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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#15 2014-05-15 01:55:02
- ShivamS
- Member
- Registered: 2011-02-07
- Posts: 3,648
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
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'
I'm not crazy, my mother had me tested.
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#17 2014-05-15 02:01:38
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
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.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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#18 2014-05-15 02:04:49
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'
I'm not crazy, my mother had me tested.
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#19 2014-05-15 02:07:22
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: Need Urgent Help!!
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.
Always satisfy the Prime Directive of getting the right answer above all else.
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#20 2014-05-15 02:08:42
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'
I'm not crazy, my mother had me tested.
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#21 2014-05-15 02:10:45
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
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.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: Need Urgent Help!!
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.
Always satisfy the Prime Directive of getting the right answer above all else.
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#24 2014-05-15 05:47:46
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'
I'm not crazy, my mother had me tested.
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#25 2014-05-15 05:49:28
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: Need Urgent Help!!
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.
Always satisfy the Prime Directive of getting the right answer above all else.
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