Lane Nguyen
04/22/2023 · Primary School
22. \( 9 d^{2}+5 d^{3}-12+3 d^{3}+7 d^{3} \)
UpStudy ThothAI Solution
Tutor-Verified Answer
Step-by-step Solution
To simplify the expression \( 9 d^{2} + 5 d^{3} - 12 + 3 d^{3} + 7 d^{3} \), we can combine like terms.
First, let's group the terms by their degree:
- The \( d^2 \) term: \( 9 d^2 \)
- The \( d^3 \) terms: \( 5 d^3 + 3 d^3 + 7 d^3 \)
- The constant term: \( -12 \)
Now, let's combine the \( d^3 \) terms:
\[
5 d^3 + 3 d^3 + 7 d^3 = (5 + 3 + 7) d^3 = 15 d^3
\]
Now we can rewrite the expression with the combined terms:
\[
9 d^2 + 15 d^3 - 12
\]
Finally, we can rearrange the terms in standard form (usually written in descending order of the degree):
\[
15 d^3 + 9 d^2 - 12
\]
Thus, the simplified expression is:
\[
\boxed{15 d^3 + 9 d^2 - 12}
\]
Quick Answer
The simplified expression is \( 15 d^3 + 9 d^2 - 12 \).
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