Johnston Li
03/14/2024 · High School
Simplify: \( 6 n\left(5 n^{2}-7 n+5\right) \) A. \( 30 n^{3}+42 n^{2}-30 n \) в. \( 30 n^{3}+30 n \) с. \( 30 n^{2}+42 n+30 \) D. \( 30 n^{3}-42 n^{2}+30 n \)
UpStudy ThothAI Solution
Tutor-Verified Answer
Step-by-step Solution
To simplify the expression \( 6 n(5 n^{2}-7 n+5) \), we will distribute \( 6n \) to each term inside the parentheses.
1. Distributing \( 6n \) to \( 5n^2 \):
\[
6n \cdot 5n^2 = 30n^3
\]
2. Distributing \( 6n \) to \( -7n \):
\[
6n \cdot (-7n) = -42n^2
\]
3. Distributing \( 6n \) to \( 5 \):
\[
6n \cdot 5 = 30n
\]
Now, we combine all the terms together:
\[
30n^3 - 42n^2 + 30n
\]
Thus, the simplified expression is:
\[
30n^3 - 42n^2 + 30n
\]
Looking at the options provided, the correct answer is:
**D. \( 30 n^{3}-42 n^{2}+30 n \)**.
Quick Answer
The simplified expression is \( 30 n^{3}-42 n^{2}+30 n \).
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