### Instruction: If $(x + y)^2 = 1$ and $xy = -4$, what is the value of $x^2 + y^2$?### Response: I notice that the expression $x^2 + y^2$ is part of the expansion of $(x + y)^2$, so I might be able to use that identity to simplify the problem.
Using the identity $(x + y)^2 = x^2 + 2xy + y^2$, I can substitute the given values of $(x + y)^2$ and $xy$ to get:

$1 = x^2 + 2(-4) + y^2$