What is expand (2(3t^2+1-2t^3))/(e^{2t)} ?

The solution to expand (2(3t^2+1-2t^3))/(e^{2t)} is (6t^2)/(e^{2t)}+2/(e^{2t)}-(4t^3)/(e^{2t)}

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expand (2(3t^2+1-2t^3))/(e^{2t)}

expand

\frac{2 ( 3 t ^{2} + 1 - 2 t ^{3} )}{e ^{2 t}}

\frac{6 t ^{2}}{e ^{2 t}} + \frac{2}{e ^{2 t}} - \frac{4 t ^{3}}{e ^{2 t}}

Solution steps

\frac{2 ( 3 t ^{2} + 1 - 2 t ^{3} )}{e ^{2 t}}

Expand

2 (3 t^{2} + 1 - 2 t^{3}) : 6 t^{2} + 2 - 4 t^{3}

= \frac{6 t ^{2} + 2 - 4 t ^{3}}{e ^{2 t}}

Apply the fraction rule:

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

\frac{6 t ^{2} + 2 - 4 t ^{3}}{e ^{2 t}} = \frac{6 t ^{2}}{e ^{2 t}} + \frac{2}{e ^{2 t}} - \frac{4 t ^{3}}{e ^{2 t}}

= \frac{6 t ^{2}}{e ^{2 t}} + \frac{2}{e ^{2 t}} - \frac{4 t ^{3}}{e ^{2 t}}

\frac{2 e ^{- s}}{( s + 1 ) ( s ^{2} + 1 )}

(2 x + 2)^{8}

e^{x} (1 + e^{x})

\frac{2 s + 1}{( s + 3 ) ( s ^{2} + 4 s + 13 )}

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

What is expand (2(3t^2+1-2t^3))/(e^{2t)} ?
The solution to expand (2(3t^2+1-2t^3))/(e^{2t)} is (6t^2)/(e^{2t)}+2/(e^{2t)}-(4t^3)/(e^{2t)}