Pregunta
17. \( \left(2 x^{2}+3 y^{2}-z^{2}\right)-\left(x^{2}-y^{2}-z^{2}\right)+\left(4 x^{2}-3 y^{2}\right) \)
Ask by Daniels Schwartz. in the United States
Jan 23,2025
Solución de tutoría real
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The simplified expression is \(5x^{2}+y^{2}\).
Solución
Calculate or simplify the expression \( (2x^2+3y^2-z^2)-(x^2-y^2-z^2)+(4x^2-3y^2) \).
Simplify the expression by following steps:
- step0: Solution:
\(\left(2x^{2}+3y^{2}-z^{2}\right)-\left(x^{2}-y^{2}-z^{2}\right)+\left(4x^{2}-3y^{2}\right)\)
- step1: Remove the parentheses:
\(2x^{2}+3y^{2}-z^{2}-\left(x^{2}-y^{2}-z^{2}\right)+4x^{2}-3y^{2}\)
- step2: Remove the parentheses:
\(2x^{2}+3y^{2}-z^{2}-x^{2}+y^{2}+z^{2}+4x^{2}-3y^{2}\)
- step3: Calculate:
\(5x^{2}+y^{2}\)
The simplified expression is \(5x^{2}+y^{2}\).
Revisado y aprobado por el equipo de tutoría de UpStudy
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Simplifique esta solución The Deep Dive
To simplify the expression \( (2 x^{2}+3 y^{2}-z^{2})-(x^{2}-y^{2}-z^{2})+(4 x^{2}-3 y^{2}) \), let's first distribute the negative sign in the second term: \[ (2 x^{2}+3 y^{2}-z^{2}) - x^{2} + y^{2} + z^{2} + (4 x^{2}-3 y^{2}). \] Now, combine like terms: 1. For \(x^2\): - \(2x^2 - x^2 + 4x^2 = (2 - 1 + 4)x^2 = 5x^2\) 2. For \(y^2\): - \(3y^2 + y^2 - 3y^2 = (3 + 1 - 3)y^2 = 1y^2 = y^2\) 3. For \(z^2\): - \(-z^2 + z^2 = 0\) Combining everything, we get: \[ 5x^{2} + y^{2}. \] Thus, the simplified expression is \[ \boxed{5x^2 + y^2}. \]
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