Which of the following statements are true?
a) $\underset{a\in\mathbb R}\forall \; \underset{b\in\mathbb R}\forall (a+b)^2=a^2+2ab+b^2$

b) $\underset{x\in\mathbb R}\exists \;\underset{y\in\mathbb R}\forall xy<1$

c) $\underset{x\in\mathbb Z^+}\exists \; \underset{y\in\mathbb Z^+}\exists \; \underset{z\in\mathbb Z^+}\exists x^3+y^3=z^3$

d)$\underset{x\in\mathbb R}\forall \; \underset{y\in\mathbb R}\exists xy<0$

e)  $\underset{x\in\mathbb R}\forall \; \underset{y\in\mathbb R^+}\exists x^2-1>y$