This problem addresses some common algebraic errors. For the equalities stated below assume that $x$ and $y$ stand for real numbers. Assume that any denominators are non-zero. Mark the equalities with T (true) if they are true for all values of $x$ and $y$, and F (false) otherwise.

$(x+y)^2 = x^2 + y^2$.
$(x+y)^2 = x^2 + 2xy+y^2$.
$\frac{x}{ x+y} = \frac{1}{y}$.
$x-(x+y) = y$.
$\sqrt{x^2} = x$.
$\sqrt{x^2} = |x|$.
$\sqrt{x^2+4} = x+2$.
$\frac{1}{x+y} = \frac{1}{x} + \frac{1}{y}$.