I'm not sure how to solve the following tasks:
Let $K\subset M$ be a field extension of a field $K$ and $x,y\in M$ are algebraic over $K$. Let $G(T_1, T_2)\in K[T_1,T_2]$ and $z=G(x,y)\in M$.
1) Show that $z$ is algebraic over $K$.
2)Let $f_x(X), f_y(X), f_z(X) \in K[X]$ be the minimal polynomials of $x,y$ and $z$. Show that $deg(f_z) \le deg(f_x)*deg(f_y)$.
English isn't my first language and I'm not sure if I got the right translations, so I'll include our definitions:
A field extension of a field $K$ is a ring homomorphism $a:K \to L$ where $L$ is also a field.
Let $K \subset L$ be a field extension. An element $x \in L$ is algebraic over $K$ if there exists a $f(T) \in K[T]$, $f\neq 0$, with $f(x)=0$.
Thanks in advance for any help.