To make [tex]\( y \)[/tex] the subject of the formula given by the equation [tex]\( w = x - 2yz^2 \)[/tex], follow these detailed steps:
1. Start with the given equation:
[tex]\[
w = x - 2yz^2
\][/tex]
2. Isolate the term involving [tex]\( y \)[/tex]:
- Move [tex]\( x \)[/tex] to the left side by subtracting [tex]\( x \)[/tex] from both sides:
[tex]\[
w - x = -2yz^2
\][/tex]
3. Eliminate the negative sign from [tex]\( -2yz^2 \)[/tex]:
- Multiply both sides by [tex]\( -1 \)[/tex]:
[tex]\[
x - w = 2yz^2
\][/tex]
4. Solve for [tex]\( y \)[/tex]:
- Divide both sides by [tex]\( 2z^2 \)[/tex] to isolate [tex]\( y \)[/tex]:
[tex]\[
y = \frac{x - w}{2z^2}
\][/tex]
Thus, the correct expression for [tex]\( y \)[/tex] as the subject of the formula is:
[tex]\[
y = \frac{x - w}{2z^2}
\][/tex]
Therefore, the correct option is:
B: [tex]\( y = \frac{x - w}{2z^2} \)[/tex]
