Solve:-
i) $x^{3} - x^{2} + x - 1$
ii) $4 x^{2} - y^{2} - 8 y z - 16 x z$

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Solution

Part (1),

$x^{3} - x^{2} + x - 1$

$= x^{2} (x - 1) + 1 (x - 1)$

$= (x - 1) (x^{2} + 1)$

Part (2),

$4 x^{2} - y^{2} - 8 y z - 16 x z$

$= {(2 x)}^{2} - y^{2} - 8 y z - 16 x z$

$= (2 x + y) (2 x - y) - 8 z (y + 2 x)$

$= (2 x + y) (2 x - y - 8 z)$

Hence, this is the answer.

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