Difference between revisions of "Common factorizations"
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== Advanced Factorizations == | == Advanced Factorizations == | ||
+ | *<math>a^2+b^2+c^2-ab-ac-bc=((a-b)^2+(b-c)^2+(c-a)^2)/2</math> | ||
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*<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> | ||
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== Other Resources == | == Other Resources == |
Revision as of 09:54, 3 May 2009
These are common factorizations that are used all the time. These should be memorized, but one should also know how they are derived.
Contents
[hide]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.