To determine the value of [tex]\( a^2 - b^2 \)[/tex] given [tex]\( a = 8 \)[/tex] and [tex]\( b = 7 \)[/tex], follow these steps:
1. Calculate [tex]\( a^2 \)[/tex]:
[tex]\[
a^2 = 8^2 = 64
\][/tex]
2. Calculate [tex]\( b^2 \)[/tex]:
[tex]\[
b^2 = 7^2 = 49
\][/tex]
3. Subtract [tex]\( b^2 \)[/tex] from [tex]\( a^2 \)[/tex]:
[tex]\[
a^2 - b^2 = 64 - 49
\][/tex]
4. Compute the result:
[tex]\[
64 - 49 = 15
\][/tex]
The value of [tex]\( a^2 - b^2 \)[/tex] is [tex]\(\boxed{15}\)[/tex].
So, the correct answer from the given options is:
\begin{tabular}{|l|l}
\hline
[tex]$(a)$[/tex] & 15 \\
\hline
[tex]$(b)$[/tex] & 20 \\
\hline
[tex]$(c)$[/tex] & 24 \\
\hline
[tex]$(d)$[/tex] & 28 \\
\hline
[tex]$(e)$[/tex] & 27 \\
\hline
\end{tabular}
