Let $E$ be an extension of $F$ and let $a,b\in E$. Prove that $F(a,b)=F(a)(b)=F(b)(a)$.

Question

Let $E$ be an extension of $F$ and let $a,b\in E$. Prove that $F(a,b)=F(a)(b)=F(b)(a)$.

My thought process is to assume $a,b\in F$, then use the associative property of multiplication. Seems simple... too simple.