(sin a + cos a )2 + (sin a - cos a)2

To simplify \((\sin a + \cos a)^2 + (\sin a - \cos a)^2\), we can expand both terms.

1. Expand \((\sin a + \cos a)^2\): \[ (\sin a + \cos a)^2 = \sin^2 a + 2\sin a \cos a + \cos^2 a \]

2. Expand \((\sin a - \cos a)^2\): \[ (\sin a - \cos a)^2 = \sin^2 a - 2\sin a \cos a + \cos^2 a \]

Now, we can add these expanded forms together: \[ (\sin^2 a + 2\sin a \cos a + \cos^2 a) + (\sin^2 a - 2\sin a \cos a + \cos^2 a) \]

Combine like terms: \[ \sin^2 a + \cos^2 a + \sin^2 a + \cos^2 a + 2\sin a \cos a - 2\sin a \cos a \] This simplifies to: \[ 2\sin^2 a + 2\cos^2 a \]

Using the Pythagorean identity \(\sin^2 a + \cos^2 a = 1\): \[ 2(\sin^2 a + \cos^2 a) = 2 \cdot 1 = 2 \]

Thus, the result is: \[ \boxed{2} \]