Let's simplify the expression [tex]\(\pi \sqrt{3} - 8 \pi \sqrt{3}\)[/tex] step by step.
1. Identify Like Terms: Notice that both terms involve [tex]\(\pi \sqrt{3}\)[/tex].
2. Factor Out the Common Factor: To simplify, we can factor out [tex]\(\pi \sqrt{3}\)[/tex] from both terms.
[tex]\[
\pi \sqrt{3} - 8 \pi \sqrt{3} = (\pi \sqrt{3})(1) - (\pi \sqrt{3})(8)
\][/tex]
3. Combine Like Terms: Now combine the like terms by subtracting the coefficients.
[tex]\[
(\pi \sqrt{3})(1 - 8) = (\pi \sqrt{3})(-7)
\][/tex]
4. Simplified Expression:
[tex]\[
-7 \pi \sqrt{3}
\][/tex]
Having simplified the expression, we see that [tex]\(-7 \pi \sqrt{3}\)[/tex] matches one of the given options.
Now, let's match our result with the options given:
A. [tex]\( -7 \sqrt{3} \pi \)[/tex]
B. [tex]\( -9 \sqrt{3} \pi \)[/tex]
C. [tex]\( -7 \pi \)[/tex]
D. [tex]\( -9 \pi \)[/tex]
Clearly, the simplified form of [tex]\(\pi \sqrt{3} - 8 \pi \sqrt{3}\)[/tex] is [tex]\( -7 \pi \sqrt{3}\)[/tex], which corresponds to option A.
Therefore, the correct answer is:
- A. [tex]\( -7 \sqrt{3} \pi \)[/tex]
