Let's focus on filling in the missing values [tex]\( U \)[/tex], [tex]\( V \)[/tex], and [tex]\( W \)[/tex] in the table corresponding to [tex]\( a - b \)[/tex].
We are given:
[tex]\[
\begin{array}{|c|c|c|c|}
\hline
a & b & a+b & a-b \\
\hline
1 & 2 & 3 & -1 \\
\hline
-1 & -2 & -3 & U \\
\hline
-4 & 1 & -3 & V \\
\hline
-6 & -3 & -9 & W \\
\hline
\end{array}
\][/tex]
### Finding [tex]\( U \)[/tex]
For [tex]\( a = -1 \)[/tex] and [tex]\( b = -2 \)[/tex]:
[tex]\[ a - b = -1 - (-2) = -1 + 2 = 1 \][/tex]
So, [tex]\( U = 1 \)[/tex].
### Finding [tex]\( V \)[/tex]
For [tex]\( a = -4 \)[/tex] and [tex]\( b = 1 \)[/tex]:
[tex]\[ a - b = -4 - 1 = -5 \][/tex]
So, [tex]\( V = -5 \)[/tex].
### Finding [tex]\( W \)[/tex]
For [tex]\( a = -6 \)[/tex] and [tex]\( b = -3 \)[/tex]:
[tex]\[ a - b = -6 - (-3) = -6 + 3 = -3 \][/tex]
So, [tex]\( W = -3 \)[/tex].
Thus, the completed table is:
[tex]\[
\begin{array}{|c|c|c|c|}
\hline
a & b & a+b & a-b \\
\hline
1 & 2 & 3 & -1 \\
\hline
-1 & -2 & -3 & 1 \\
\hline
-4 & 1 & -3 & -5 \\
\hline
-6 & -3 & -9 & -3 \\
\hline
\end{array}
\][/tex]
