Difference between revisions of "Common factorizations"
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− | These are | + | These are '''common factorizations'''. |
+ | <!-- | ||
+ | I think the formatting looks bad. Bulleted equations just don't look | ||
+ | good. Maybe \begin{align*} . . . \end{align*} would be good. The equations | ||
+ | should at least be centered. | ||
+ | --> | ||
− | *<math> | + | ==Basic Factorizations== |
+ | *<math>x^2-y^2=(x+y)(x-y)</math> | ||
− | *<math> | + | *<math>x^3+y^3=(x+y)(x^2-xy+y^2)</math> |
− | *<math> | + | *<math>x^3-y^3=(x-y)(x^2+xy+y^2)</math> |
+ | |||
+ | == Vieta's/Newton Factorizations == | ||
+ | |||
+ | <!-- What exactly do these relations have to do with Vieta's relations? --> | ||
+ | These factorizations are useful for problem that could otherwise be solved by [[Newton sums]] or problems that give a polynomial, and ask a question about the roots. Combined with [[Vieta's formulas]], these are excellent, useful factorizations. | ||
+ | |||
+ | *<math>(a+b+c)^2=a^2+b^2+c^2+2(ab+bc+ac)</math> | ||
+ | |||
+ | *<math>(a+b+c)^3=a^3+b^3+c^3+3(a+b)(b+c)(a+c)</math> | ||
+ | |||
+ | == Esoteric Identities == | ||
+ | *<math>a^2+b^2+c^2-ab-ac-bc=((a-b)^2+(b-c)^2+(c-a)^2)/2</math> <!-- This isn't a factorization . . . --> | ||
+ | |||
+ | *<math>a^3+b^3+c^3-3abc=(a+b+c)(a^2+b^2+c^2-ab-ac-bc)</math> | ||
+ | |||
+ | == Other Resources == | ||
+ | |||
+ | * [http://tutorial.math.lamar.edu/pdf/Algebra_Cheat_Sheet_Reduced.pdf More Factorizations] <!-- Do we really have to link to something like this? | ||
+ | Isn't AoPS supposed to be beyond formula sheets? | ||
+ | --> | ||
+ | |||
+ | [[Category:Algebra]] |
Revision as of 13:05, 14 July 2021
These are common factorizations.
Contents
Basic Factorizations
Vieta's/Newton Factorizations
These factorizations are useful for problem that could otherwise be solved by Newton sums or problems that give a polynomial, and ask a question about the roots. Combined with Vieta's formulas, these are excellent, useful factorizations.