Factorize:
$(a + b) (c + d) - a^{2} + b^{2}$

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Solution

$(a + b) (c + d) - a^{2} + b^{2}$

$= (a + b) (c + d) + b^{2} - a^{2}$

$= (a + b) (c + d) - (a + b) (a - b)$

$= (a + b) (- a + b + c + d)$

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