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

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Solution

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

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