What is expand (0.4+0.6e^t)^3 ?

The solution to expand (0.4+0.6e^t)^3 is 0.064+0.288e^t+0.432e^{2t}+0.216e^{3t}

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expand (0.4+0.6e^t)^3

expand

(0.4 + 0.6 e^{t})^{3}

0.064 + 0.288 e^{t} + 0.432 e^{2 t} + 0.216 e^{3 t}

Solution steps

(0.4 + 0.6 e^{t})^{3}

Apply Perfect Cube Formula:

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

a = 0.4, b = 0.6 e^{t}

= 0. 4^{3} + 3 \cdot 0. 4^{2} \cdot 0.6 e^{t} + 3 \cdot 0.4 (0.6 e^{t})^{2} + (0.6 e^{t})^{3}

Simplify

0. 4^{3} + 3 \cdot 0. 4^{2} \cdot 0.6 e^{t} + 3 \cdot 0.4 (0.6 e^{t})^{2} + (0.6 e^{t})^{3} : 0.064 + 0.288 e^{t} + 0.432 e^{2 t} + 0.216 e^{3 t}

= 0.064 + 0.288 e^{t} + 0.432 e^{2 t} + 0.216 e^{3 t}

e^{t} (H (t) - H (t - 1))

\frac{\partial}{\partial x} ((u) (3 x (x - 1)))

(5, 6, 8) - (7 i + 6 j)

2 x + y (cos (t)) + (2 y + x) e^{t}

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

What is expand (0.4+0.6e^t)^3 ?
The solution to expand (0.4+0.6e^t)^3 is 0.064+0.288e^t+0.432e^{2t}+0.216e^{3t}