Merging Rows and Columns for a Table

Question

I have to create this table in LaTeX but I don't like the current way it looks right now. Here is what I want it to look like when I compile the code,

And this is the current code that I have along with the LaTeX output

\begin{tabular}{|c|c|c|c|c|}
    \hline
    & & \multicolumn{3}{c|}{\textbf{Mother}}\\
    \hline
    & & $u_n$ & $v_n$ & $0.5w_n$\\
    \hline
    & $u_n$ & $u_n^2$ & $u_nv_n$ & $0.5u_nw_n$\\
    \hline
    \textbf{Father} & $v_n$ & $u_nv_n$ & $v_n^2$ & $0.5v_nw_n$\\
    \hline
    & $0.5w_n$ & $0.5u_nw_n$ & $0.5v_nw_n$ & $0.25w_n^2$\\
    \hline
\end{tabular}

Answer 1

You can get this table, even without nesting the two environments multicolumn and multirow (to use this latter, you need the package with the same name):

\documentclass{article}
\usepackage{multirow}

\begin{document}
\begin{tabular}{|c|c|c|c|c|}
  \hline
  \multicolumn{2}{|c|}{}                      & \multicolumn{3}{c|}{\textbf{Mother}}\\
  \cline{3-5}
  \multicolumn{2}{|c|}{}                      & $u_n$       & $v_n$       & $0.5w_n$\\
  \hline
  \multirow{3}{*}{\textbf{Father}} & $u_n$    & $u_n^2$     & $u_nv_n$    & $0.5u_nw_n$\\
  \cline{2-5}
                                   & $v_n$    & $u_nv_n$    & $v_n^2$     & $0.5v_nw_n$\\
  \cline{2-5}
                                   & $0.5w_n$ & $0.5u_nw_n$ & $0.5v_nw_n$ & $0.25w_n^2$\\
  \hline
\end{tabular}
\end{document}

Answer 2

The tabularray packages makes such layouts really easy:

\documentclass{article}

\usepackage{tabularray}

\begin{document}

\begin{tblr}{
    hlines,
    vlines,
    colspec={ccccc},
    cells={mode=math},
    cell{1}{3}={mode=text,font=\bfseries},
    cell{3}{1}={mode=text,font=\bfseries}
}
    \SetCell[c=2,r=2]{} & & \SetCell[c=3]{} Mother\\
    & & u_n & v_n & 0.5w_n\\
    \SetCell[r=3]{} Father & u_n & u_n^2 & u_nv_n & 0.5u_nw_n\\
    & v_n & u_nv_n & v_n^2 & 0.5v_nw_n\\
    & 0.5w_n & 0.5u_nw_n & 0.5v_nw_n & 0.25w_n^2\\
\end{tblr}

\end{document}