Difference between revisions of "Common factorizations"
m (→Advanced Factorizations) |
m |
||
| Line 1: | Line 1: | ||
| − | These are ''common factorizations'' | + | 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. | ||
| + | --> | ||
==Basic Factorizations== | ==Basic Factorizations== | ||
| Line 10: | Line 15: | ||
== Vieta's/Newton 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 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)^2=a^2+b^2+c^2+2(ab+bc+ac)</math> | ||
| Line 16: | Line 22: | ||
*<math>(a+b+c)^3=a^3+b^3+c^3+3(a+b)(b+c)(a+c)</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> | + | *<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> | *<math>a^3+b^3+c^3-3abc=(a+b+c)(a^2+b^2+c^2-ab-ac-bc)</math> | ||
| Line 23: | Line 29: | ||
== Other Resources == | == Other Resources == | ||
| − | * [http://tutorial.math.lamar.edu/pdf/Algebra_Cheat_Sheet_Reduced.pdf More | + | * [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:Elementary algebra]] | [[Category:Elementary algebra]] | ||
Revision as of 23:02, 3 May 2009
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.
