Question
Expand \( \omega^{5}\left(\omega^{4}+3\right) \)
Ask by May Smith. in the United Arab Emirates
Mar 02,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The expanded expression is \( \omega^9 + 3\omega^5 \).
Solution
To expand ω⁵(ω⁴ + 3), distribute ω⁵ to each term inside the parentheses:
ω⁵ · ω⁴ = ω⁹
ω⁵ · 3 = 3ω⁵
Thus, the expanded expression is:
ω⁹ + 3ω⁵
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Simplify this solution Bonus Knowledge
To expand \( \omega^{5}(\omega^{4}+3) \), we can distribute \( \omega^{5} \) across the terms inside the parentheses. First, we multiply \( \omega^{5} \) by \( \omega^{4} \): \[ \omega^{5} \cdot \omega^{4} = \omega^{5+4} = \omega^{9} \] Next, we multiply \( \omega^{5} \) by \( 3 \): \[ \omega^{5} \cdot 3 = 3\omega^{5} \] Now, we can combine these results: \[ \omega^{5}(\omega^{4}+3) = \omega^{9} + 3\omega^{5} \] Thus, the final expanded expression is: \[ \omega^{9} + 3\omega^{5} \]
