Pregunta
e. \( 5 P^{2}\left(P^{4}+1\right)+\left(5 P^{3}\right)^{2} \)
Ask by Conner Pope. in the United States
Mar 12,2025
Solución de inteligencia artificial de Upstudy
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The simplified expression is \(30P^{6}+5P^{2}\).
Solución
Calculate or simplify the expression \( 5*P^2*(P^4+1)+(5*P^3)^2 \).
Simplify the expression by following steps:
- step0: Solution:
\(5P^{2}\left(P^{4}+1\right)+\left(5P^{3}\right)^{2}\)
- step1: Expand the expression:
\(5P^{6}+5P^{2}+\left(5P^{3}\right)^{2}\)
- step2: Rewrite the expression:
\(5P^{6}+5P^{2}+25P^{6}\)
- step3: Add the terms:
\(30P^{6}+5P^{2}\)
The simplified expression is \(30P^{6}+5P^{2}\).
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Simplifique esta solución Extra Insights
Let’s break it down! The expression \( 5 P^{2}(P^{4} + 1) + (5 P^{3})^{2} \) can be expanded as follows: First, we multiply \( 5 P^{2} \) by \( P^{4} + 1 \): \[ 5 P^{2} \cdot P^{4} + 5 P^{2} \cdot 1 = 5 P^{6} + 5 P^{2} \] Next, we tackle \( (5 P^{3})^{2} \): \[ (5 P^{3})^{2} = 25 P^{6} \] Now, combining both parts, we have: \[ 5 P^{6} + 5 P^{2} + 25 P^{6} = (5 P^{6} + 25 P^{6}) + 5 P^{2} = 30 P^{6} + 5 P^{2} \] So, the simplified form of the expression is: \[ 30 P^{6} + 5 P^{2} \] Happy computing!
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