  We present new short proofs to both the exact and the stability results of
two extremal problems. The first one is the extension of Tur\'{a}n's theorem in
hypergraphs, which was firstly studied by Mubayi $\cite{MU06}$. The second one
is about the cancellative hypergraphs, which was firstly studied by
Bollob\'{a}s $\cite{BO74}$ and later by Keevash and Mubayi $\cite{KM04}$. Our
proofs are concise and straightforward, but give a sharper version of stability
theorems to both problems.
