$(x^{2} - 4 y^{2}) \div (x + 2 y) = ?$

x + 2y

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x - 2y

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x + 4y

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x - 4y

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Solution

The correct option is B
x - 2y

We know that $(a^{2} - b^{2}) = (a + b) (a - b)$

Thus, $x^{2} - 4 y^{2}$

$= x^{2} - (2 y)^{2}$

$= (x + 2 y) (x - 2 y)$

So, when $x^{2} - 4 y^{2}$ is divided by $(x + 2 y)$ we get $(x - 2 y)$

i.e $\frac{x^{2} - 4 y^{2}}{(x + 2 y)} = \frac{(x + 2 y) (x - 2 y)}{(x + 2 y)} = (x - 2 y)$

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