Pregunta
Which of the following is equivalent to the difference: \( \left(-3 x^{2}+5 x-1\right)-\left(4 x^{2}-3 x+7\right) \) (1) \( 7 x^{2}-8 x+8 \) (2) \( -7 x^{2}+8 x-8 \) (3) \( x^{2}+2 x-8 \) (4) \( -x^{2}-2 x+8 \)
Ask by Peterson Guerrero. in the United States
Mar 13,2025
Solución de inteligencia artificial de Upstudy
Respuesta verificada por el tutor
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The difference is \( -7x^{2}+8x-8 \), so the correct answer is (2) \( -7 x^{2}+8 x-8 \).
Solución
Calculate or simplify the expression \( (-3x^2+5x-1)-(4x^2-3x+7) \).
Simplify the expression by following steps:
- step0: Solution:
\(\left(-3x^{2}+5x-1\right)-\left(4x^{2}-3x+7\right)\)
- step1: Remove the parentheses:
\(-3x^{2}+5x-1-\left(4x^{2}-3x+7\right)\)
- step2: Remove the parentheses:
\(-3x^{2}+5x-1-4x^{2}+3x-7\)
- step3: Subtract the terms:
\(-7x^{2}+8x-8\)
The difference \( \left(-3 x^{2}+5 x-1\right)-\left(4 x^{2}-3 x+7\right) \) is equivalent to \( -7x^{2}+8x-8 \).
Therefore, the correct answer is (2) \( -7 x^{2}+8 x-8 \).
Respondido por UpStudy AI y revisado por un tutor profesional
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Simplifique esta solución The Deep Dive
To find the equivalent expression for the difference \( \left(-3 x^{2}+5 x-1\right)-\left(4 x^{2}-3 x+7\right) \), we first need to distribute the negative sign across the second polynomial: \[ -3x^{2} + 5x - 1 - 4x^{2} + 3x - 7 \] Now, combine like terms: 1. For the \( x^{2} \) terms: \(-3x^{2} - 4x^{2} = -7x^{2}\) 2. For the \( x \) terms: \(5x + 3x = 8x\) 3. For the constant terms: \(-1 - 7 = -8\) Putting it all together, we have: \[ -7x^{2} + 8x - 8 \] So, the equivalent expression is: (2) \( -7 x^{2}+8 x-8 \)
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