Using the identity $(x + y)^{2} + (x - y)^{2} = 2 (x^{2} + y^{2})$

Compute the value of $4^{2} + 2^{2}$

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Solution

The correct option is C
20

The given expression is

$4^{2} + 2^{2}$

$= (3 + 1)^{2} + (3 - 1)^{2}$

$= 2 (3^{2} + 1^{2}) [(x + y)^{2} + (x - y)^{2} = 2 (x^{2} + y^{2})]$

$= 2 (9 + 1)$

$= 2 \times 10$

$= 20$

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