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1. $a^{2} + b^{2}$

Answer: Option B

Explanation:

a^{2} + b^{2} = \frac{1}{2} \{{(a + b)}^{2} + {(a - b)}^{2}\} = \frac{1}{2} (4^{2} + 2^{2}) = \frac{1}{2} (16 + 4) = \frac{1}{2} \times 20 = 10

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