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

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Solution

The equation $x^{2} + x y + x z + y z$ can be factorised as follows:

$x^{2} + x y + x z + y z = (x^{2} + x y) + (x z + y z) = x (x + y) + z (x + y) = (x + z) (x + y)$

Hence, $x^{2} + x y + x z + y z = (x + z) (x + y)$

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