# Factoring Formulas

Factoring is nothing but breaking down a number or a polynomial into product of its factor which when multiplied together gives the original.

Factoring Formula for sum/difference of two nth powers are,

### Product Formulas

$\large a^{2}−b^{2}=(a−b)(a+b)$

$\large a^{3}−b^{3}=(a−b)(a^{2}+ab+b^{2})$

$\large a^{3}+b^{3}=(a+b)(a^{2}−ab+b^{2})$

$\large a^{4}-b^{4}=(a-b)(a+b)(a^{2}−ab+b^{2})$

$\large a^{5}−b^{5}=(a−b)(a^{4}+a^{3}b+a^{2}b^{2}+ab^{3}+b^{4})$

Product Formulas

$\large (a+b)^{2}=a^{2}+2ab+b^{2}$

$\large (a-b)^{2}=a^{2}-2ab+b^{2}$

$\large (a+b)^{3}=a^{3}+3a^{2}b+3ab^{2}+b^{3}$

$\large (a−b)^{3}=a^{3}−3a^{2}b+3ab^{2}−b^{3}$

$\large (a+b)^{4}=a^{4}+4a^{3}b+6a^{2}b^{2}+4ab^{3}+b^{4}$

$\large (a-b)^{4}=a^{4}-4a^{3}b+6a^{2}b^{2}-4ab^{3}+b^{4}$

$\large (a+b+c)^{2}=a^{2}+b^{2}+c^{2}+2ab+2ac+2bc$

$\large (a+b+c+…)^{2}=a^{2}+b^{2}+c^{2}+…+2(ab+ac+bc+…)$

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