# Factorization formula

by ehrenfest
Tags: factorization, formula
 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 = (x-y)(x^199+x^198y+... + y^198*x + y^199) ? 2. Relevant equations 3. The attempt at a solution
 P: 1,345 Not that I've ever heard... $$(x+y)(x-y)(x^2+y^2)(x^4+y^4)(x^4+x^3y+x^{2}y^2+xy^3+y^4)(x^4-x^3y+x^2y^2-xy^3+y^4)(x^8-x^6y^2+x^4y^4-x^2y^6+y^8)(x^{16}-x^{12}y^4+x^8y^8-x^4y^{12}+y^{16})$$ $$(x^{20}+x^{15}y^5+x^{10}y^{10}+x^5y^{15}+y^{20})(x^{20}-x^{15}y^5+x^{10}y^{10}-x^5y^{15}+y^{20})(x^{40}-x^{30}y^{10}+x^{20}y^{20}-x^{10}y^{30}+y^{40})$$ $$(x^{80}-x^{60}y^{20}+x^{40}y^{40}-x^{20}y^{60}+y^{80})$$ 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...
 P: 1,754 which calculator do you have? i been thinking about upgrading to a TI-89 ...
P: 1,345
Factorization formula

 Quote by rocophysics which calculator do you have? i been thinking about upgrading to a TI-89 ...
Ti-89 Titanium
Math
Emeritus
Thanks
PF Gold
P: 39,682
 Quote by ehrenfest 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 = (x-y)(x^199+x^198y+... + y^198*x + y^199) ?
Do you mean
$$x^n- y^n= (x-y)(x^{n-1}+ x^(n-2)y+ /cdot/cdot/cdot+ xy^{n-2}+ y^{n-1}$$?
I've never worried about it having a name!
P: 1,996
 Quote by HallsofIvy Do you mean $$x^n- y^n= (x-y)(x^{n-1}+ x^(n-2)y+ /cdot/cdot/cdot+ xy^{n-2}+ y^{n-1}$$? I've never worried about it having a name!
Yes. I just forget identities so easily when I have to remember them by their statement not some label. However, you're right, this is a pretty simple one that is easily verifiable and probably doesn't warrant a name!

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