Question - Algebraic Expression Simplification
Solution:
\[
\begin{array}{l}
\text{Given: } y + \frac{1}{y} = b \\
\text{Squaring both sides: } \\
\left( y + \frac{1}{y} \right)^2 = b^2 \\
y^2 + 2 \cdot y \cdot \frac{1}{y} + \left( \frac{1}{y} \right)^2 = b^2 \\
y^2 + 2 + \frac{1}{y^2} = b^2 \\
\text{Subtract 2 from both sides: } \\
y^2 + \frac{1}{y^2} = b^2 - 2
\end{array}
\]
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