Let a and b be real numbers such that a + b = -1. Compute a^2 - b^2 + 3a + b.
a^2 - b^2 = (a + b) ( a - b) = (-1) (a - b)
So
a^2 - b^2 + 3a + b =
(-1)(a - b) + 3a + b =
-a + b + 3a + b =
2a + 2b =
2 (a + b) =
2 (-1) =
-2
