x(1-x^2)^1/2
You asked:
Evaluate the expression: \(\frac{{\left( x \cdot \left(1 - {x}^{2}\right) \right)}^{1}}{2}\)
MathBot Answer:
Evaluated
\(\displaystyle \frac{{\left( x \cdot \left(1 - {x}^{2}\right) \right)}^{1}}{2} = \frac{x \left(1 - x^{2}\right)}{2} \)
Expanded
\[\frac{{\left( x \cdot \left(1 - {x}^{2}\right) \right)}^{1}}{2} = - \frac{x^{3}}{2} + \frac{x}{2}\]
Factored
\[\frac{{\left( x \cdot \left(1 - {x}^{2}\right) \right)}^{1}}{2} = - \frac{x \left(x - 1\right) \left(x + 1\right)}{2}\]