$(\frac{z+z^{-1}}{2})^4 $ simplified
You asked:
Simplify the expression: \({\left( \frac{z + {z}^{-1}}{2} \right)}^{4}\)
MathBot Answer:
Simplified:
\[ {\left( \frac{z + {z}^{-1}}{2} \right)}^{4} = \frac{\left(z^{2} + 1\right)^{4}}{16 z^{4}} \]
Expanded:
\[ {\left( \frac{z + {z}^{-1}}{2} \right)}^{4} = \frac{z^{4}}{16} + \frac{z^{2}}{4} + \frac{3}{8} + \frac{1}{4 z^{2}} + \frac{1}{16 z^{4}} \]
Factored:
\[ {\left( \frac{z + {z}^{-1}}{2} \right)}^{4} = \frac{\left(z^{2} + 1\right)^{4}}{16 z^{4}} \]