Simplify the expression:
$(a + b)^{2} + (a - b)^{2}$

2 (a^{2} + b^{2})

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(a^{2} + b^{2})

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2 (a^{2} - b^{2})

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(a^{2} - b^{2})

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Solution

The correct option is A $2 (a^{2} + b^{2})$
The above expression can be written as,
$(a + b)^{2} + (a - b)^{2}$
$= (a^{2} + 2 a b + b^{2}) + (a^{2} - 2 a b + b^{2})$
Rearranging the terms, we get,
$a^{2} + a^{2} + 2 a b - 2 a b + b^{2} + b^{2}$
$= 2 a^{2} + 2 b^{2}$
$= 2 (a^{2} + b^{2})$

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