Difference between revisions of "Common factorizations"
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| − | These are | + | == Basic Factorizations == |
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| + | These are basic factorizations that are used all the time. These should be memorized, but you one should also know where they are derived from. | ||
*<math>\displaystyle x^2-y^2=(x+y)(x-y)</math> | *<math>\displaystyle x^2-y^2=(x+y)(x-y)</math> | ||
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*<math>\displaystyle x^3-y^3=(x-y)(x^2+xy+y^2)</math> | *<math>\displaystyle x^3-y^3=(x-y)(x^2+xy+y^2)</math> | ||
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| + | == 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. | ||
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| + | *<math>\displaystyle (a+b+c)^2=a^2+b^2+c^2+2(ab+bc+ac)</math> | ||
*<math>\displaystyle (a+b+c)^3=a^3+b^3+c^3+3(a+b)(b+c)(a+c)</math> | *<math>\displaystyle (a+b+c)^3=a^3+b^3+c^3+3(a+b)(b+c)(a+c)</math> | ||
| − | + | == Other Resources == | |
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| + | * [http://tutorial.math.lamar.edu/pdf/Algebra_Cheat_Sheet_Reduced.pdf More Common Factorizations]. | ||
Revision as of 16:09, 20 June 2006
Basic Factorizations
These are basic factorizations that are used all the time. These should be memorized, but you one should also know where they are derived from.
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.
