확장 (0.4+0.6e^t)^3

해법

확장

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

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

솔루션 단계

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

완벽한 큐브 공식 적용:

(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}

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}

단순화하세요:

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}