4x^{\frac{-1}{2}}\left(x^{\frac{5}{2}}-x^{\frac{-3}{2}}\right)
You asked:
Evaluate the expression: \(4 \cdot {x}^{\frac{-1}{2}} \cdot \left({x}^{\frac{5}{2}} - {x}^{\frac{-3}{2}}\right)\)
MathBot Answer:
Evaluated
\(\displaystyle 4 \cdot {x}^{\frac{-1}{2}} \cdot \left({x}^{\frac{5}{2}} - {x}^{\frac{-3}{2}}\right) = \frac{4 \left(x^{\frac{5}{2}} - \frac{1}{x^{\frac{3}{2}}}\right)}{\sqrt{x}} \)
Expanded
\[4 \cdot {x}^{\frac{-1}{2}} \cdot \left({x}^{\frac{5}{2}} - {x}^{\frac{-3}{2}}\right) = 4 x^{2} - \frac{4}{x^{2}}\]
Factored
\[4 \cdot {x}^{\frac{-1}{2}} \cdot \left({x}^{\frac{5}{2}} - {x}^{\frac{-3}{2}}\right) = \frac{4 \left(x^{2} + 1\right) \left(x - 1\right) \left(x + 1\right)}{x^{2}}\]