Let's complete the table by calculating the sums (\(a + b\)) and the differences (\(a - b\)).
Here is the step-by-step breakdown for each pair of \(a\) and \(b\):
1. Pair (-5, -16):
- Sum (\(a + b\)):
[tex]\[
-5 + (-16) = -21
\][/tex]
- Difference (\(a - b\)):
[tex]\[
-5 - (-16) = -5 + 16 = 11
\][/tex]
2. Pair (6, -18):
- Sum (\(a + b\)):
[tex]\[
6 + (-18) = -12
\][/tex]
- Difference (\(a - b\)):
[tex]\[
6 - (-18) = 6 + 18 = 24
\][/tex]
3. Pair (-12, 24):
- Sum (\(a + b\)):
[tex]\[
-12 + 24 = 12
\][/tex]
- Difference (\(a - b\)):
[tex]\[
-12 - 24 = -36
\][/tex]
4. Pair (18, 31):
- Sum (\(a + b\)):
[tex]\[
18 + 31 = 49
\][/tex]
- Difference (\(a - b\)):
[tex]\[
18 - 31 = -13
\][/tex]
5. Pair (-25, -17):
- Sum (\(a + b\)):
[tex]\[
-25 + (-17) = -42
\][/tex]
- Difference (\(a - b\)):
[tex]\[
-25 - (-17) = -25 + 17 = -8
\][/tex]
6. Pair (31, -41):
- Sum (\(a + b\)):
[tex]\[
31 + (-41) = -10
\][/tex]
- Difference (\(a - b\)):
[tex]\[
31 - (-41) = 31 + 41 = 72
\][/tex]
Now, we can fill in the table with the calculated values:
[tex]\[
\begin{tabular}{|c|c|c|c|}
\hline
[tex]$a$[/tex] & [tex]$b$[/tex] & [tex]$a + b$[/tex] & [tex]$a - b$[/tex] \\
\hline
-5 & -16 & -21 & 11 \\
\hline
6 & -18 & -12 & 24 \\
\hline
-12 & 24 & 12 & -36 \\
\hline
18 & 31 & 49 & -13 \\
\hline
-25 & -17 & -42 & -8 \\
\hline
31 & -41 & -10 & 72 \\
\hline
\end{tabular}
\][/tex]
