展开 (e^{2t}+2e^t)^3

解答

展开

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

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

求解步骤

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

使用完全立方公式:

(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}

化简

(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}

e x p an d a (3, - 2, 1) b (6, 1, - 2)

e x p an d 200 (1 - e^{- k (5)})

e x p an d 6 (- \frac{2}{3})^{4} + 2 (- \frac{2}{3})^{3} - 12 (- \frac{2}{3})^{2} + 3

e x p an d a (2, - 1, 0) + b (5, 5, - 2) + c (0, 1, 1)

s im pl i f y 8 x^{2} + 4 x - 2 \cdot (\frac{x ^{5}}{5} + \frac{x ^{3}}{3})