The expression $16 x^{4} - 81 y^{4}$ is NOT evenly divisible by

2 x - 3 y

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2 x + 3 y

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4 x - 9 y

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4 x^{2} + 9 y^{2}

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Solution

The correct option is D $4 x - 9 y$
Here, first check the option for the equation $16 x^{4} - 81 y^{4}$
$\Rightarrow (4 x^{2})^{2} - (9 y^{2})^{2}$
$a^{2} - b^{2} = (a + b) (a - b)$
$\Rightarrow (4 x^{2} + 9 y^{2}) (4 x^{2} - 9 y^{2})$
$\Rightarrow 2 x - 3 y, 2 x + 3 y, 4 x^{2} + 9 y^{2}$ are the factors of $16 x^{4} - 81 y^{4}$
So, $4 x - 9 y$ is not evenly divisible.

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