Find the factors of the following expression:
$9 x^{2} y^{2} - 16$

(3 x y - 4)

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(2 x y - 3)

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(3 x y + 4)

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(2 x y + 3)

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Solution

The correct options are
A $(3 x y - 4)$
C $(3 x y + 4)$
$9 x^{2} y^{2} - 16$
$= (3 x y)^{2} - 4^{2} [∵ a^{2} - b^{2} = (a + b) (a - b)]$
$= (3 x y + 4) (3 x y - 4)$
Hence, factors of $9 x^{2} y^{2} - 16$ are $(3 x y + 4)$ and $(3 x y - 4)$ .

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