Factorise : $a^{2} + 4 a + 4 - b^{2}$

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Solution

$a^{2} + 4 a + 4 - b^{2} {\begin{matrix} ∵ (a + b)^{2} = a^{2} + 2 a b + b^{2} a^{2} - b^{2} = (a + b) (a - b) \end{matrix}} = (a)^{2} + 2 \times a \times 2 + (2)^{2} - (b)^{2} = (a + 2)^{2} - (b)^{2} = (a + 2 + b) (a + 2 - b) = (a + b + 2) (a - b + 2)$

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