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

The solution to expand (e^{2t}+2e^t)^3 is e^{6t}+6e^{5t}+12e^{4t}+8e^{3t}

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expand (e^{2t}+2e^t)^3

expand

(e^{2 t} + 2 e^{t})^{3}

e^{6 t} + 6 e^{5 t} + 12 e^{4 t} + 8 e^{3 t}

Solution steps

(e^{2 t} + 2 e^{t})^{3}

Apply Perfect Cube Formula:

(a + b)^{3} = a^{3} + 3 a^{2} b + 3 a b^{2} + b^{3}

a = e^{2 t}, b = 2 e^{t}

= (e^{2 t})^{3} + 3 (e^{2 t})^{2} \cdot 2 e^{t} + 3 e^{2 t} (2 e^{t})^{2} + (2 e^{t})^{3}

Simplify

(e^{2 t})^{3} + 3 (e^{2 t})^{2} \cdot 2 e^{t} + 3 e^{2 t} (2 e^{t})^{2} + (2 e^{t})^{3} : e^{6 t} + 6 e^{5 t} + 12 e^{4 t} + 8 e^{3 t}

= e^{6 t} + 6 e^{5 t} + 12 e^{4 t} + 8 e^{3 t}

a (3, - 2, 1) b (6, 1, - 2)

200 (1 - e^{- k (5)})

6 (- \frac{2}{3})^{4} + 2 (- \frac{2}{3})^{3} - 12 (- \frac{2}{3})^{2} + 3

a (2, - 1, 0) + b (5, 5, - 2) + c (0, 1, 1)

8 x^{2} + 4 x - 2 \cdot (\frac{x ^{5}}{5} + \frac{x ^{3}}{3})

What is expand (e^{2t}+2e^t)^3 ?
The solution to expand (e^{2t}+2e^t)^3 is e^{6t}+6e^{5t}+12e^{4t}+8e^{3t}