Difference between revisions of "Common factorizations"
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*<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> | ||
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| + | == Advanced Factorizations == | ||
| + | *<math>a^3+b^3+c^3-3abc=(a+b+c)(a^2+b^2+c^2-ab-ac-bc)=(a+b+c)((a-b)^2+(b-c)^2+(c-a)^2)/2</math> | ||
== Other Resources == | == Other Resources == | ||
Revision as of 10:53, 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
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.
