Factorise : $16 - x^{2} - 2 x y - y^{2}$ The factors are

(4 + x - y) (4 + x + y)

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(4 - x - y) (4 - x + y)

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(2 + x + y) (2 - x - y)

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(4 + x + y) (4 - x - y)

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Solution

The correct option is D $(4 + x + y) (4 - x - y)$
Given, $16 - x^{2} - 2 x y - y^{2}$
$= 4^{2} - [x^{2} + 2 x y + y^{2}]$
$= 4^{2} - (x + y)^{2}$
By using $a^{2} - b^{2} = (a + b) (a - b)$
$∴ 4^{2} - (x + y)^{2} = (4 + x + y) (4 - x - y)$

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