Factorisation Formula

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

$a^{2} + 2 a b + b^{2} = (a + b)^{2}$

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

$a^{3} + b^{3} = (a + b) (a^{2} - a b + b^{2})$

$a^{3} - b^{3} = (a - b) (a^{2} + a b + b^{2})$

$x^{2} + b x + c = (x + m) (x + n)$

$a x + a y + b x + b y = (a + b) (x + y)$

$x^{2} + b x + c = (x + r) (x + s)$

$a b + a c = a (b + c)$

$a^{n} - b^{n} = (a - b) (a^{n - 1} + a^{n - 2} b + \dots + b^{n - 1})$

$a^{4} - b^{4} = (a^{2} - b^{2}) (a^{2} + b^{2}) = (a - b) (a + b) (a^{2} + b^{2})$

$a^{3} + b^{3} + c^{3} - 3 a b c = (a + b + c) (a^{2} + b^{2} + c^{2} - a b - b c - c a)$

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

$(a - b)^{3} = a^{3} - 3 a^{2} b + 3 a b^{2} - b^{3}$

$a x^{2} + b x + c = (m x + n) (p x + q)$

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