Factorise:

$x^{2} - y^{2} - 4 x z + 4 z^{2}$

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Solution

$x^{2} - y^{2} - 4 x z + 4 z^{2} = x^{2} - 4 x z + 4 z^{2} - y^{2} = (x)^{2} - 2 \times x 2 z + (2 z)^{2} - (y)^{2} = (x - 2 z)^{2} - (y)^{2} = (x - 2 z + y) (x - 2 z - y) = (x + y - 2 z) (x - y - 2 z)$

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