Common factorizations

Basic Factorizations

These are basic factorizations that are used all the time. These should be memorized, but one should also know how they are derived.

$\displaystyle x^2-y^2=(x+y)(x-y)$

$\displaystyle x^3+y^3=(x+y)(x^2-xy+y^2)$

$\displaystyle x^3-y^3=(x-y)(x^2+xy+y^2)$

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.

$\displaystyle (a+b+c)^2=a^2+b^2+c^2+2(ab+bc+ac)$

$\displaystyle (a+b+c)^3=a^3+b^3+c^3+3(a+b)(b+c)(a+c)$

Other Resources

More Common Factorizations.

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Common factorizations

Basic Factorizations

Vieta's/Newton Factorizations

Other Resources