Factorise: $9 x^{2} - 6 x y + y^{2} - z^{2}$

(3 x - y + z) (3 x - y - z)

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(3 x + y - z) (3 x - y - z)

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(3 x + y + z) (3 x - y - z)

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None of these

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Solution

The correct option is A $(3 x - y + z) (3 x - y - z)$
The value of $9 x^{2} - 6 x y + y^{2} - z^{2}$
$= (9 x^{2} - 6 x y + y^{2}) - z^{2}$
$= {(3 x)^{2} - 2 \times 3 x \times y + y^{2}} - z^{2}$
$= (3 x - y^{2}) - z^{2}$
$= (3 x - y + z) (3 x - y - z)$
Hence, option A is correct.

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