What is expand ((1+2e^t)^3)/(27) ?

The solution to expand ((1+2e^t)^3)/(27) is 1/27+(2e^t)/9+(4e^{2t})/9+(8e^{3t})/(27)

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expand ((1+2e^t)^3)/(27)

expand

\frac{( 1 + 2 e ^{t} ) ^{3}}{27}

\frac{1}{27} + \frac{2 e ^{t}}{9} + \frac{4 e ^{2 t}}{9} + \frac{8 e ^{3 t}}{27}

Solution steps

\frac{( 1 + 2 e ^{t} ) ^{3}}{27}

(1 + 2 e^{t})^{3} = 1 + 6 e^{t} + 12 e^{2 t} + 8 e^{3 t}

= \frac{1 + 6 e ^{t} + 12 e ^{2 t} + 8 e ^{3 t}}{27}

Apply the fraction rule:

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

\frac{1 + 6 e ^{t} + 12 e ^{2 t} + 8 e ^{3 t}}{27} = \frac{1}{27} + \frac{6 e ^{t}}{27} + \frac{12 e ^{2 t}}{27} + \frac{8 e ^{3 t}}{27}

= \frac{1}{27} + \frac{6 e ^{t}}{27} + \frac{12 e ^{2 t}}{27} + \frac{8 e ^{3 t}}{27}

Cancel

\frac{6 e ^{t}}{27} : \frac{2 e ^{t}}{9}

= \frac{1}{27} + \frac{2 e ^{t}}{9} + \frac{12 e ^{2 t}}{27} + \frac{8 e ^{3 t}}{27}

Cancel

\frac{12 e ^{2 t}}{27} : \frac{4 e ^{2 t}}{9}

= \frac{1}{27} + \frac{2 e ^{t}}{9} + \frac{4 e ^{2 t}}{9} + \frac{8 e ^{3 t}}{27}

\frac{I n ( 2 - 3 x )}{x ^{2} - 36}

(3 (n + 1))!

(x + 2)^{2}

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

(x + 1) (x - x + 1)

What is expand ((1+2e^t)^3)/(27) ?
The solution to expand ((1+2e^t)^3)/(27) is 1/27+(2e^t)/9+(4e^{2t})/9+(8e^{3t})/(27)