Which of the following is not a factor of $144 x^{2} - 96 x y + 16 y^{2}$

(3 x - y)

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(9 x - y)

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{(3 x - y)}^{2}

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(48 x - 16 y)

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Solution

The correct option is B $(9 x - y)$
$144 x^{2} - 96 x y + 16 y^{2}$
$= 16 ({9 x}^{2} - 6 x y + y^{2})$
$= 16 {(3 x - y)}^{2}$ ... $(∵ {(a - b)}^{2} = a^{2} - 2 a b + b^{2})$
$= 16 (3 x - y) (3 x - y)$
$= (48 x - 16 y) (3 x - y)$

From above, only $(9 x - y)$ is not a factor of the given expression.

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