Davison Logan
09/16/2023 · Junior High School
3) \( \begin{array}{l}\mathrm{f}(\mathrm{a})=3 \mathrm{a} \\ \mathrm{g}(\mathrm{a})=\mathrm{a}^{3}+3 \mathrm{a}^{2} \\ \text { Find } \mathrm{f}(\mathrm{a}) \times \\ \mathrm{g}(\mathrm{a})\end{array} \)
UpStudy ThothAI Solution
Tutor-Verified Answer
Step-by-step Solution
To find \( f(a) \times g(a) \), we first need to evaluate \( f(a) \) and \( g(a) \) using the given functions.
1. The function \( f(a) \) is defined as:
\[
f(a) = 3a
\]
2. The function \( g(a) \) is defined as:
\[
g(a) = a^3 + 3a^2
\]
Now, we can calculate \( f(a) \times g(a) \):
\[
f(a) \times g(a) = (3a) \times (a^3 + 3a^2)
\]
Next, we distribute \( 3a \) across the terms in \( g(a) \):
\[
f(a) \times g(a) = 3a \cdot a^3 + 3a \cdot 3a^2
\]
Calculating each term:
- The first term:
\[
3a \cdot a^3 = 3a^4
\]
- The second term:
\[
3a \cdot 3a^2 = 9a^3
\]
Now, we combine the results:
\[
f(a) \times g(a) = 3a^4 + 9a^3
\]
Thus, the final result is:
\[
\boxed{3a^4 + 9a^3}
\]
Quick Answer
\( 3a^4 + 9a^3 \)
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