(1+x/2-2/x)^4

asked by guest
on Nov 19, 2024 at 4:43 am



You asked:

Evaluate the expression: \({\left( 1 + \frac{x}{2} - \frac{2}{x} \right)}^{4}\)

MathBot Answer:

Evaluated



\(\displaystyle {\left( 1 + \frac{x}{2} - \frac{2}{x} \right)}^{4} = \left(\frac{x}{2} + 1 - \frac{2}{x}\right)^{4} \)

Expanded

\[{\left( 1 + \frac{x}{2} - \frac{2}{x} \right)}^{4} = \frac{x^{4}}{16} + \frac{x^{3}}{2} + \frac{x^{2}}{2} - 4 x - 5 + \frac{16}{x} + \frac{8}{x^{2}} - \frac{32}{x^{3}} + \frac{16}{x^{4}}\]

Factored

\[{\left( 1 + \frac{x}{2} - \frac{2}{x} \right)}^{4} = \frac{\left(x^{2} + 2 x - 4\right)^{4}}{16 x^{4}}\]

+ Submit Question