Pregunta
Factor completely: \( 3 u^{4} y^{4}-3 u^{4} \)
Ask by Pearson Wells. in the United States
Jan 18,2025
Solución de inteligencia artificial de Upstudy
Respuesta verificada por el tutor
Responder
The expression \(3u^{4}y^{4}-3u^{4}\) factors to \(3u^{4}(y-1)(y+1)(y^{2}+1)\).
Solución
Factor the expression \( 3u^4y^4-3u^4 \).
Factor the expression by following steps:
- step0: Factor:
\(3u^{4}y^{4}-3u^{4}\)
- step1: Factor the expression:
\(3u^{4}\left(y^{4}-1\right)\)
- step2: Factor the expression:
\(3u^{4}\left(y^{2}-1\right)\left(y^{2}+1\right)\)
- step3: Evaluate:
\(3u^{4}\left(y-1\right)\left(y+1\right)\left(y^{2}+1\right)\)
The factored form of the expression \(3u^{4}y^{4}-3u^{4}\) is \(3u^{4}(y-1)(y+1)(y^{2}+1)\).
Respondido por UpStudy AI y revisado por un tutor profesional
Como
error msg
Explicar 
Simplifique esta solución The Deep Dive
To factor \( 3 u^{4} y^{4}-3 u^{4} \), we can start by noticing that both terms share a common factor of \( 3 u^{4} \). We can factor this out: \[ 3 u^{4}(y^{4} - 1) \] Next, \( y^{4} - 1 \) is a difference of squares, which can be further factored: \[ y^{4} - 1 = (y^{2} - 1)(y^{2} + 1) \] And \( y^{2} - 1 \) itself is also a difference of squares: \[ y^{2} - 1 = (y - 1)(y + 1) \] Putting it all together, we arrive at the complete factorization: \[ 3 u^{4}(y - 1)(y + 1)(y^{2} + 1) \]
¡Prueba Premium ahora!
¡Prueba Premium y hazle a Thoth AI preguntas de matemáticas ilimitadas ahora!
Quizas mas tarde
Hazte Premium
