$Simply the equation y = (a + 1)^{2} + (a - 1)^{2}$ .
For a = 4, value of y is

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Solution

The correct option is A 34
$Given , y = (a + 1)^{2} + (a - 1)^{2}$

$∵ (a + b)^{2} = a^{2} + b^{2} + 2 a b$

$(a + 1)^{2} + (a - 1)^{2} ⟹ a^{2} + 1 + 2 a + a^{2} + 1 - 2 a$

$⟹ 2 a^{2} + 2$
$⟹ 2 (a^{2} + 1)$

Substituting a = 4,

$We get : 2 (4^{2} + 1) = 2 (17) = 34$

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