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Algebraic Identities

Factorise: x2...

Question

Factorise:
$x^{2} + y^{2} - z^{2} - 2 x y$

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Solution

$= x^{2} + y^{2} - z^{2} - 2 x y = x^{2} + y^{2} - 2 x y - z^{2} = (x - y)^{2} - z^{2}$
since $(a^{2} - 2 a b + b^{2}) = (a - b)^{2}$

$= (x - y + z) (x - y - z)$ since $(a^{2} - b^{2}) = (a + b) (a - b)$

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