Certainly! Let's simplify the expression [tex]\(\frac{8 y^2+4 y-1}{2}\)[/tex] step-by-step.
### Step 1: Understand the Expression
We start with the expression [tex]\(\frac{8 y^2 + 4 y - 1}{2}\)[/tex].
### Step 2: Distribute the Denominator
We need to divide each term in the numerator by the denominator. The given denominator is 2. So, each term in the numerator ([tex]\(8y^2\)[/tex], [tex]\(4y\)[/tex], and [tex]\(-1\)[/tex]) should be divided by 2 individually.
### Step 3: Perform the Division
Let's divide each term in the numerator by 2:
1. Divide [tex]\(8y^2\)[/tex] by 2:
[tex]\[
\frac{8y^2}{2} = 4y^2
\][/tex]
2. Divide [tex]\(4y\)[/tex] by 2:
[tex]\[
\frac{4y}{2} = 2y
\][/tex]
3. Divide [tex]\(-1\)[/tex] by 2:
[tex]\[
\frac{-1}{2} = -\frac{1}{2}
\][/tex]
### Step 4: Combine the Results
Now, combine the results of each division:
[tex]\[
4y^2 + 2y - \frac{1}{2}
\][/tex]
### Final Expression
The simplified form of the given expression [tex]\(\frac{8 y^2 + 4 y - 1}{2}\)[/tex] is:
[tex]\[
4y^2 + 2y - \frac{1}{2}
\][/tex]
So, the final simplified expression is:
[tex]\[
4y^2 + 2y - \frac{1}{2}
\][/tex]
