Free and bound variables
In the usual mathematical notation: $(\lambda \color{blue}{x}. (\&amp; (f_1 \color{green}{x}) (f_2 \color{green}{x}))) A$

The two green occurrences of $\color{green}{x}$ in the subterms $f_1 \color{green}{x}$ and $f_2 \color{green}{x}$ are bound in the term $\lambda \color{blue}{x}. (\&amp; (f_1 \color{green}{x}) (f_2 \color{green}{x}))$. The binding occurrence is the blue $\color{blue}{x}$.

When evaluation $(\lambda \color{blue}{x}. (\&amp; (f_1 \color{green}{x}) (f_2 \color{green}{x}))) A$ by beta-reduction of the top redex, the result is the substitution of $A$ for the free occurrences of $x$ in the body of the lambda abstraction. If $\&amp;$, $f_1$ and $f_2$ are variables, then the result is simply
$$ (\lambda \color{blue}{x}. (\&amp; (f_1 \color{green}{x}) (f_2 \color{green}{x}))) A  \to_{\beta} (\&amp; (f_1 A) (f_2 A)) $$
If $\&amp;$, $f_1$ and $f_2$ are lambda-terms, then they may contain free occurrences of $x$, which need to be substituted.
$$ (\lambda \color{blue}{x}. (\&amp; (f_1 \color{green}{x}) (f_2 \color{green}{x}))) A  \to_{\beta} (\&amp;[x\leftarrow A] (f_1[x\leftarrow A] A) (f_2[x\leftarrow A] A)) $$

Note that the notion of free or bound variable is really a free or bound occurrence of a variable, in a given term. A variable is often said to be free in a term if it has a free occurrence. For example, in the term $(\lambda \color{blue}{x}. (\&amp; (f_1 \color{green}{x}) (f_2 \color{green}{x}))) (g \, \color{magenta}{x})$, the green occurrences of $\color{green}{x}$ are bound, and the magenta occurrence of $\color{magenta}{x}$ is free. In the term $\&amp; (f_1 \color{green}{x}) (f_2 \color{green}{x}))$, the two occurrences of $\color{green}{x}$ are free.