Factorise:

Question:

Factorise:

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

 

Solution:

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

$=\left(x^{2}+y^{2}-2 x y\right)-z^{2}$

$=(x-y)^{2}-z^{2} \quad\left[a^{2}-2 a b+b^{2}=(a-b)^{2}\right]$

$=(x-y+z)(x-y-z) \quad\left[a^{2}-b^{2}=(a+b)(a-b)\right]$

 

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