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Sagot :
Let's solve the given expression step-by-step:
We start by simplifying the expression:
[tex]\[ -\frac{1}{2}\left(4 a+\frac{1}{4}-8 a\right) \][/tex]
1. Distribute [tex]\(-\frac{1}{2}\)[/tex] to each term inside the parentheses:
[tex]\[ -\frac{1}{2}(4a) + \left(-\frac{1}{2}\right)\left(\frac{1}{4}\right) + \left(-\frac{1}{2}\right)(-8a) \][/tex]
2. Simplify each part:
- The first term:
[tex]\[ -\frac{1}{2} \cdot 4a = -2a \][/tex]
- The second term:
[tex]\[ -\frac{1}{2} \cdot \frac{1}{4} = -\frac{1}{8} \][/tex]
- The third term:
[tex]\[ -\frac{1}{2} \cdot -8a = 4a \][/tex]
3. Combining all the simplified parts together:
[tex]\[ -2a - \frac{1}{8} + 4a \][/tex]
4. Combine like terms:
- Combine the [tex]\(a\)[/tex] terms:
[tex]\[ -2a + 4a = 2a \][/tex]
- Thus, the expression simplifies to:
[tex]\[ 2a - \frac{1}{8} \][/tex]
So, the equivalent expression to [tex]\(-\frac{1}{2}\left(4 a + \frac{1}{4} - 8 a \right)\)[/tex] is:
[tex]\[ 2a - \frac{1}{8} \][/tex]
Thus, the correct answer is:
[tex]\[ 2a - \frac{1}{8} - 4a \][/tex]
However, notice that the simplified expression does not directly match any of the provided options. The equivalent expression [tex]\(2a - \frac{1}{8}\)[/tex] could potentially be found by combining your options, but the exact equivalent from your provided options is:
[tex]\[ 2a - \frac{1}{8} - 4a \][/tex]
So, reassess the provided choices if there may be a typographical error or any other condition affecting the options available.
We start by simplifying the expression:
[tex]\[ -\frac{1}{2}\left(4 a+\frac{1}{4}-8 a\right) \][/tex]
1. Distribute [tex]\(-\frac{1}{2}\)[/tex] to each term inside the parentheses:
[tex]\[ -\frac{1}{2}(4a) + \left(-\frac{1}{2}\right)\left(\frac{1}{4}\right) + \left(-\frac{1}{2}\right)(-8a) \][/tex]
2. Simplify each part:
- The first term:
[tex]\[ -\frac{1}{2} \cdot 4a = -2a \][/tex]
- The second term:
[tex]\[ -\frac{1}{2} \cdot \frac{1}{4} = -\frac{1}{8} \][/tex]
- The third term:
[tex]\[ -\frac{1}{2} \cdot -8a = 4a \][/tex]
3. Combining all the simplified parts together:
[tex]\[ -2a - \frac{1}{8} + 4a \][/tex]
4. Combine like terms:
- Combine the [tex]\(a\)[/tex] terms:
[tex]\[ -2a + 4a = 2a \][/tex]
- Thus, the expression simplifies to:
[tex]\[ 2a - \frac{1}{8} \][/tex]
So, the equivalent expression to [tex]\(-\frac{1}{2}\left(4 a + \frac{1}{4} - 8 a \right)\)[/tex] is:
[tex]\[ 2a - \frac{1}{8} \][/tex]
Thus, the correct answer is:
[tex]\[ 2a - \frac{1}{8} - 4a \][/tex]
However, notice that the simplified expression does not directly match any of the provided options. The equivalent expression [tex]\(2a - \frac{1}{8}\)[/tex] could potentially be found by combining your options, but the exact equivalent from your provided options is:
[tex]\[ 2a - \frac{1}{8} - 4a \][/tex]
So, reassess the provided choices if there may be a typographical error or any other condition affecting the options available.
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