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The resultant of $7 x^{2} - 8 y^{2}$ is:

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$(\sqrt{7} x + \sqrt{8} y) (\sqrt{7} x - \sqrt{8} y)$

${(\sqrt{7} x - \sqrt{8} y)}^{2}$

$(7 x + 8 y) (7 x + 8 y)$

$(7 x + 8 y) (7 x - 8 y)$

answer is C.

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Detailed Solution

$7 x^{2} - 8 y^{2}$ = $49 x^{2} - 64 y^{2}$

As we know $a^{2} - b^{2} = (a + b) (a - b)$

$7 x^{2} - 8 y^{2} =$ ${(\sqrt{7})}^{2} x^{2} - {(\sqrt{8})}^{2} y^{2}$

$=$ $(\sqrt{7} x + \sqrt{8} y) (\sqrt{7} x - \sqrt{8} y)$

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