# S.O.S. Mathematics CyberBoard

Your Resource for mathematics help on the web!
 It is currently Sat, 30 Jul 2016 17:48:41 UTC

 All times are UTC [ DST ]

 Page 1 of 1 [ 8 posts ]
 Print view Previous topic | Next topic
Author Message
 Post subject: Cubic factorisationPosted: Tue, 20 Dec 2011 01:17:34 UTC
 Senior Member

Joined: Thu, 21 Apr 2011 03:44:05 UTC
Posts: 57
Location: Depends where I am
Hello all,

Can someone please tell m,e what I am doing wrong here?? I cannot seem to get it right...

The question is:

...........I dont really know what happens here as the answer apparently should be

Any help would be greatly appreciated

Thanks

Top

 Post subject: Re: Cubic factorisationPosted: Tue, 20 Dec 2011 01:20:18 UTC
 Moderator

Joined: Wed, 30 Mar 2005 04:25:14 UTC
Posts: 15397
Location: Austin, TX
Where did you get the xy term in your initial factorization?

In any case, your mistake is in your first step, you have a -2(x-1) where you should have a +2(x+1).

_________________
(\ /)
(O.o)
(> <)
This is Bunny. Copy Bunny into your signature to help him on his way to world domination

Top

 Post subject: Re: Cubic factorisationPosted: Tue, 20 Dec 2011 01:45:39 UTC
 Senior Member

Joined: Thu, 21 Apr 2011 03:44:05 UTC
Posts: 57
Location: Depends where I am

I'm sorry, I don't think I understand you.

Firstly, the term came from the . Also, how do you get ??? Doesn't a '' and a '' make a ''?

Thanks

Top

 Post subject: Re: Cubic factorisationPosted: Tue, 20 Dec 2011 03:43:46 UTC
 Member of the 'S.O.S. Math' Hall of Fame

Joined: Sun, 24 Jul 2005 20:12:39 UTC
Posts: 4852
Location: Ottawa Ontario
gareth wrote:
The question is:

a^3 - b^3 = (a - b)(a^2 + xy + b^2)
The xy you have in there should be ab; that the standard way to
show the difference of cubes; use it as a GUIDE ONLY

Start this way: let k = x + 1; then your expression becomes k^3 - 2^3;
now factor that, using a^3 - b^3 = (a - b)(a^2 + ab + b^2) as a GUIDE:
k^3 - 2^3 = (k - 2)(k^2 + 2k + 2^2)
Now substitute x-1 back in and finish off...

_________________
I'm just an imagination of your figment...

Top

 Post subject: Re: Cubic factorisationPosted: Tue, 20 Dec 2011 06:47:28 UTC
 Moderator

Joined: Wed, 30 Mar 2005 04:25:14 UTC
Posts: 15397
Location: Austin, TX
gareth wrote:

I'm sorry, I don't think I understand you.

Firstly, the term came from the . Also, how do you get ??? Doesn't a '' and a '' make a ''?

Thanks

No, I get a +2(x+1), you have and , multiply them and you get and the formula we have (the correct version) tells us we need to add that, so naturally I did.

_________________
(\ /)
(O.o)
(> <)
This is Bunny. Copy Bunny into your signature to help him on his way to world domination

Top

 Post subject: Re: Cubic factorisationPosted: Wed, 21 Dec 2011 20:02:36 UTC
 Member of the 'S.O.S. Math' Hall of Fame

Joined: Wed, 10 Jan 2007 19:16:15 UTC
Posts: 666
Location: England
Or, if you wanted to be really long-winded about it (and didn't have a set method that you had to use), you could:

(2) Use the remainder theorem to find roots by substituting in divisors of 7 (which, as a prime, means ):
, so is a root is a factor

(4) Re-expand and then compare to get the coefficient of x in the quadratic term (i.e. to find the a)
:

(5) Check the discriminant of your quadratic to see if you could factorise it further
, so it can't be factorised over the reals any further.

Hence:

It's not quick and it's not pretty, but it definitely works

_________________
"It's never crowded along the extra mile"

Graduated, and done with maths forever

Top

 Post subject: Re: Cubic factorisationPosted: Fri, 13 Jan 2012 12:53:15 UTC
 Senior Member

Joined: Thu, 21 Apr 2011 03:44:05 UTC
Posts: 57
Location: Depends where I am
Hello everybody,

just getting back to my math again...

A dumb question: Going by the cubic factorisation formula, why does ???? Isn't the ??. Obviously gives the correct answer, but I thought that you subbed directly onto the formula. Why is this not so????

Any help is appreciated.

Regards

Top

 Post subject: Re: Cubic factorisationPosted: Fri, 13 Jan 2012 20:44:27 UTC
 Moderator

Joined: Wed, 30 Mar 2005 04:25:14 UTC
Posts: 15397
Location: Austin, TX
gareth wrote:
Hello everybody,

just getting back to my math again...

A dumb question: Going by the cubic factorisation formula, why does ???? Isn't the ??. Obviously gives the correct answer, but I thought that you subbed directly onto the formula. Why is this not so????

Any help is appreciated.

Regards

DIFFERENCE of cubes, not SUM.

_________________
(\ /)
(O.o)
(> <)
This is Bunny. Copy Bunny into your signature to help him on his way to world domination

Top

 Display posts from previous: All posts1 day7 days2 weeks1 month3 months6 months1 year Sort by AuthorPost timeSubject AscendingDescending
 Page 1 of 1 [ 8 posts ]

 All times are UTC [ DST ]

#### Who is online

Users browsing this forum: No registered users

 You cannot post new topics in this forumYou cannot reply to topics in this forumYou cannot edit your posts in this forumYou cannot delete your posts in this forum

Search for:
 Jump to:  Select a forum ------------------ High School and College Mathematics    Algebra    Geometry and Trigonometry    Calculus    Matrix and Linear Algebra    Differential Equations    Probability and Statistics    Proposed Problems Applications    Physics, Chemistry, Engineering, etc.    Computer Science    Math for Business and Economics Advanced Mathematics    Foundations    Algebra and Number Theory    Analysis and Topology    Applied Mathematics    Other Topics in Advanced Mathematics Other Topics    Administrator Announcements    Comments and Suggestions for S.O.S. Math    Posting Math Formulas with LaTeX    Miscellaneous