Question
Find the product. Simplify your answer. \( j^{2}\left(-3 j^{2}+j+4\right) \)
Ask by Bartlett Mcdonald. in the United States
Feb 04,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
\(-3j^{4} + j^{3} + 4j^{2}\)
Solution
To find the product of \( j^{2}\left(-3 j^{2}+j+4\right) \) and simplify it, follow these steps:
1. **Distribute \( j^2 \) to each term inside the parentheses:**
\[
j^2 \cdot (-3j^2) + j^2 \cdot j + j^2 \cdot 4
\]
2. **Multiply each term:**
\[
-3j^{4} + j^{3} + 4j^{2}
\]
3. **Write the expression in standard form (from highest to lowest degree):**
\[
-3j^{4} + j^{3} + 4j^{2}
\]
This is the simplified form of the product.
**Final Answer:**
\(-3j^{4} + j^{3} + 4j^{2}\)
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Extra Insights
To simplify the expression \( j^{2}\left(-3 j^{2}+j+4\right) \), we start by distributing \( j^2 \) across the terms inside the parenthesis. So we calculate: \[ j^2 \cdot (-3j^2) = -3j^{4} \] \[ j^2 \cdot j = j^{3} \] \[ j^2 \cdot 4 = 4j^{2} \] Now, we combine these results: \[ -3j^4 + j^3 + 4j^2 \] Thus, the simplified product is: \[ -3j^{4} + j^{3} + 4j^{2} \]
