What is expand ((2-x^2)^2)/(2e^{5x)} ?

The solution to expand ((2-x^2)^2)/(2e^{5x)} is 2/(e^{5x)}-(2x^2)/(e^{5x)}+(x^4)/(2e^{5x)}

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expand ((2-x^2)^2)/(2e^{5x)}

expand

\frac{( 2 - x ^{2} ) ^{2}}{2 e ^{5 x}}

\frac{2}{e ^{5 x}} - \frac{2 x ^{2}}{e ^{5 x}} + \frac{x ^{4}}{2 e ^{5 x}}

Solution steps

\frac{( 2 - x ^{2} ) ^{2}}{2 e ^{5 x}}

(2 - x^{2})^{2} = 4 - 4 x^{2} + x^{4}

= \frac{4 - 4 x ^{2} + x ^{4}}{2 e ^{5 x}}

Apply the fraction rule:

\frac{a \pm b}{c} = \frac{a}{c} \pm \frac{b}{c}

\frac{4 - 4 x ^{2} + x ^{4}}{2 e ^{5 x}} = \frac{4}{2 e ^{5 x}} - \frac{4 x ^{2}}{2 e ^{5 x}} + \frac{x ^{4}}{2 e ^{5 x}}

= \frac{4}{2 e ^{5 x}} - \frac{4 x ^{2}}{2 e ^{5 x}} + \frac{x ^{4}}{2 e ^{5 x}}

Divide the numbers:

\frac{4}{2} = 2

= \frac{2}{e ^{5 x}} - \frac{2 x ^{2}}{e ^{5 x}} + \frac{x ^{4}}{2 e ^{5 x}}

\frac{( x - 3 ) ( x + 4 )}{x ^{2} - 1}

\frac{4}{x ( x ^{2} + 2 )}

(1 - b) (1 + b)

(x^{3} + 89 - x^{3} + 9)^{2}

cos (\frac{( 3 n - 2 ) π}{3})

What is expand ((2-x^2)^2)/(2e^{5x)} ?
The solution to expand ((2-x^2)^2)/(2e^{5x)} is 2/(e^{5x)}-(2x^2)/(e^{5x)}+(x^4)/(2e^{5x)}