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Zeroes of a Polynomial

Factorize: ...

Question

Factorize: $x^{2} + y^{2} + x + y + 2 x y$

(x + 2 y) (2 x + 2 y + 1)

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(x + y) (x + y + 1)

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(2 x + y) (x - y + 1)

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(2 x + y) (x + y + 1)

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Solution

The correct option is A $(x + y) (x + y + 1)$
$x^{2} + y^{2} + x + y + 2 x y$
$= x^{2} + y^{2} + 2 x y + x + y$
$= (x + y)^{2} + (x + y)$
$= (x + y) (x + y + 1)$

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