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

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

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

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

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

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Solution

The correct option is D $(x + 3 y + z) (x + 3 y - z)$
The value of $x^{2} + 6 x y - z^{2} + 9 y^{2}$ is
$=$ $x^{2} + 6 x y + 9 y^{2} - z^{2}$
$=$ ${(x + 3 y)}^{2} - z^{2}$
$=$ $(x + 3 y + z) (x + 3 y - z)$ ....By using $a^{2} - b^{2} = (a - b) (a + b)$

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