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Interhalogen Compounds - Structures

Factories : ...

Question

Factories : $p^{2} + q^{2} - a^{2} - b^{2} + 2 p q + 2 a b + p + q - a + b$

A

(p + q - a + b) (p + q + a - b + 1)

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B

(p - q - a + b) (p - q + a - b + 1)

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C

(p + q + a + b) (p + q + a - b + 1)

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D

(p + q - a - b) (p + q + a - b + 1)

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Solution

The correct option is C $(p + q - a + b) (p + q + a - b + 1)$
$p^{2} + q^{2} - a^{2} - b^{2} + 2 p q + 2 a b + p + q - a + b = (p^{2} + q^{2} + 2 p q) + (p + q) - (a^{2} + b^{2} - 2 a b) - (a - b) = {(p + q)}^{2} + (p + q) - (a - b)^{2} - (a - b) = (p + q - a + b) (p + q + a - b) + (p + q - a + b) = (p + q - a + b) (p + q + a - b + 1)$

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