Some doubts regarding truth table for the function \$(cd+b'c+bd')(b+d)\$?
If your variables are \$b\$, \$c\$, and \$d\$, then your eight minterms are:

$$\begin{align}
&amp; bcd \\
&amp; bcd' \\
&amp; bc'd \\
&amp; bc'd' \\
&amp; b'cd \\
&amp; b'cd' \\
&amp; b'c'd \\
&amp; b'c'd' \\
\end{align}$$

Your formula was:

$$bcd + bd′ + cd + b′cd$$

To express this in terms of minterms, you have to fill in the missing variables. Let's look at \$bd'\$. The \$c\$ is missing, which means it has no effect on \$bd'\$. So we can write this as:

$$bd' = bcd' + bc'd'$$

You could simplify the equation first:

$$bcd + bd' + cd + b'cd = bd' + cd$$

but if you need the minterms, you'll just have to expand it again.