Let's complete the table step by step:
We are given the values for [tex]\(a\)[/tex] and [tex]\(b\)[/tex] for two pairs and need to find the sums [tex]\(a + b\)[/tex] and the differences [tex]\(a - b\)[/tex]:
### For [tex]\((-8, -2)\)[/tex]:
1. Sum Calculation [tex]\(-8 + (-2)\)[/tex]:
[tex]\[
-8 + (-2) = -8 - 2 = -10
\][/tex]
2. Difference Calculation [tex]\(-8 - (-2)\)[/tex]:
[tex]\[
-8 - (-2) = -8 + 2 = -6
\][/tex]
So for the pair [tex]\((-8, -2)\)[/tex]:
- [tex]\(a + b = -10\)[/tex]
- [tex]\(a - b = -6\)[/tex]
### For [tex]\( (4, 9) \)[/tex]:
1. Sum Calculation [tex]\(4 + 9\)[/tex]:
[tex]\[
4 + 9 = 13
\][/tex]
2. Difference Calculation [tex]\(4 - 9\)[/tex]:
[tex]\[
4 - 9 = 4 - 9 = -5
\][/tex]
So for the pair [tex]\( (4, 9) \)[/tex]:
- [tex]\(a + b = 13\)[/tex]
- [tex]\(a - b = -5\)[/tex]
### Completed Table:
[tex]\[
\begin{tabular}{|c|c|c|c|}
\hline
$a$ & $b$ & $a+b$ & $a-b$ \\
\hline
-5 & +3 & -2 & -8 \\
\hline
-8 & -2 & -10 & -6 \\
\hline
+4 & +9 & 13 & -5 \\
\hline
\end{tabular}
\][/tex]
Now the table is completed with the appropriate sums and differences for each pair of [tex]\(a\)[/tex] and [tex]\(b\)[/tex].
