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Short multiplication formulas (polynomial identities)

Algebra

Square of sum and difference, difference of squares, cube of sum and difference, sum and difference of cubes formulas.
$$\qquad{(a \pm b)^2 =a^2 \pm 2ab+b^2}$$ $$\qquad{(a \pm b)^3 =a^3 \pm 3a^2b+3ab^2 \pm b^3}$$ $$\qquad{a^2 - b^2 =(a-b)(a+b)}$$ $$\qquad{a^3 \pm b^3 = (a \pm b)(a^2 \mp ab + b^2)}$$
Binomial formula, where [tex]C^k_n=\frac{A^k_n}{k!}=\frac{n!}{k!(n-k)!}[/tex] are the binomial coefficients.
$$(a+b)^n=C_{n}^{0}a^nb^0+C_{n}^{1}a^{n-1}b^1+C_{n}^{2}a^{n-2}b^2+...+C_{n}^{n-1}a^1b^{n-1}+C_{n}^{n}a^0b^n$$

Last time edited 2017-11-06

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