Pregunta
\( 1 \ll \begin{array}{l}\begin{array}{r}5 x^{4}+6 x^{2}-2 x \\ -\left(-7 x^{4}-2 x^{2}+3 x\right)\end{array} \\ \begin{array}{l}\text { The difference is } \square . \\ \text { (Simplify your answer.) }\end{array}\end{array} \)
Ask by Bradley Curry. in the United Arab Emirates
Mar 16,2025
Solución de inteligencia artificial de Upstudy
Respuesta verificada por el tutor
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The difference is \(12x^4 + 8x^2 - 5x\).
Solución
**Step 1. Distribute the negative sign**
We start with the expression:
\[
5x^4 + 6x^2 - 2x -\left(-7x^4 - 2x^2 + 3x\right)
\]
Distribute the minus sign inside the parentheses:
\[
5x^4 + 6x^2 - 2x + 7x^4 + 2x^2 - 3x
\]
**Step 2. Combine like terms**
Group the like terms:
- For \(x^4\):
\[
5x^4 + 7x^4 = 12x^4
\]
- For \(x^2\):
\[
6x^2 + 2x^2 = 8x^2
\]
- For \(x\):
\[
-2x - 3x = -5x
\]
**Step 3. Write the simplified expression**
The simplified result is:
\[
12x^4 + 8x^2 - 5x
\]
Thus, the difference is \(12x^4 + 8x^2 - 5x\).
Respondido por UpStudy AI y revisado por un tutor profesional
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Simplifique esta solución Mind Expander
To find the difference, we start by simplifying the expression inside the parentheses: \[ 5x^{4} + 6x^{2} - 2x - \left(-7x^{4} - 2x^{2} + 3x\right) \] First, we'll distribute the negative sign: \[ 5x^{4} + 6x^{2} - 2x + 7x^{4} + 2x^{2} - 3x \] Next, we'll combine like terms: - For \(x^4\): \(5x^{4} + 7x^{4} = 12x^{4}\) - For \(x^{2}\): \(6x^{2} + 2x^{2} = 8x^{2}\) - For \(x\): \(-2x - 3x = -5x\) Putting it all together, we get: \[ 12x^{4} + 8x^{2} - 5x \] So the simplified answer for the difference is: \[ \boxed{12x^{4} + 8x^{2} - 5x} \]
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