Factoring Formulas

$a^2 - b^2 = (a-b)(a+b)$ $a^3 - b^3 = (a-b)\left(a^2 + ab + b^2\right)$ $a^3 + b^3 = (a+b)\left(a^2 - ab + b^2\right)$ $a^4 - b^4 = (a-b)(a+b)\left(a^2 + b^2\right)$ $a^5 - b^5 = (a-b)\left(a^4 + a^3b + a^2b^2 + ab^3 + b^4\right)$

Product Formulas

$(a + b)^2 = a^2 + 2ab + b^2$ $(a - b)^2 = a^2 - 2ab + b^2$ $(a + b)^3 = a^3 + 3a^2b + 3ab^2 + b^3$ $(a - b)^3 = a^3 - 3a^2b + 3ab^2 - b^3$ $(a + b)^4 = a^4 + 4a^3b + 6a^2b^2 + 4ab^3 + b^4$ $(a - b)^4 = a^4 - 4a^3b + 6a^2b^2 - 4ab^3 + b^4$ $(a + b + c)^2 = a^2 + b^2 + c^2 +2ab + 2ac + 2bc$ $(a + b + c + ...)^2 = a^2 + b^2 + c^2 + ... + 2(ab + ac + bc + ... )$