Difference between revisions of "Common factorizations"
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| − | + | These are ''common factorizations'' that are used all the time. These should be memorized, but one should also know how they are derived. | |
| − | + | ==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> |
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== Vieta's/Newton Factorizations == | == Vieta's/Newton Factorizations == | ||
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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 that show up everywhere. | 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 that show up everywhere. | ||
| − | *<math> | + | *<math>(a+b+c)^2=a^2+b^2+c^2+2(ab+bc+ac)</math> |
| − | *<math> | + | *<math>(a+b+c)^3=a^3+b^3+c^3+3(a+b)(b+c)(a+c)</math> |
== Other Resources == | == Other Resources == | ||
* [http://tutorial.math.lamar.edu/pdf/Algebra_Cheat_Sheet_Reduced.pdf More Common Factorizations]. | * [http://tutorial.math.lamar.edu/pdf/Algebra_Cheat_Sheet_Reduced.pdf More Common Factorizations]. | ||
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| + | [[Category:Elementary algebra]] | ||
Revision as of 17:03, 25 December 2007
These are common factorizations that are used all the time. These should be memorized, but one should also know how they are derived.
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 factorizations that show up everywhere.
