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Factorization formula 
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#1
Jul2807, 12:03 AM

P: 1,996

1. The problem statement, all variables and given/known data
Is there like a formula with a name easy to remember of which the following is a specific instance: x^200 y^200 = (xy)(x^199+x^198y+... + y^198*x + y^199) ? 2. Relevant equations 3. The attempt at a solution 


#2
Jul2807, 12:22 AM

P: 1,345

Not that I've ever heard...
[tex](x+y)(xy)(x^2+y^2)(x^4+y^4)(x^4+x^3y+x^{2}y^2+xy^3+y^4)(x^4x^3y+x^2y^2xy^3+y^4)(x^8x^6y^2+x^4y^4x^2y^6+y^8)(x^{16}x^{12}y^4+x^8y^8x^4y^{12}+y^{16})[/tex] [tex](x^{20}+x^{15}y^5+x^{10}y^{10}+x^5y^{15}+y^{20})(x^{20}x^{15}y^5+x^{10}y^{10}x^5y^{15}+y^{20})(x^{40}x^{30}y^{10}+x^{20}y^{20}x^{10}y^{30}+y^{40})[/tex] [tex](x^{80}x^{60}y^{20}+x^{40}y^{40}x^{20}y^{60}+y^{80})[/tex] Sorry wouldn't fint onto one line... Maybe to can find a pattern to that mess though. If not, well, it took my calculator about 3 second to find the answer, might want to use one the next time you need to factor that... 


#3
Jul2807, 12:26 AM

P: 1,754

which calculator do you have? i been thinking about upgrading to a TI89 ...



#4
Jul2807, 12:27 AM

P: 1,345

Factorization formula



#5
Jul2807, 04:31 PM

Math
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Thanks
PF Gold
P: 39,682

[tex]x^n y^n= (xy)(x^{n1}+ x^(n2)y+ /cdot/cdot/cdot+ xy^{n2}+ y^{n1}[/tex]? I've never worried about it having a name! 


#6
Jul2807, 05:02 PM

P: 1,996




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