展开 (t+e^{2t})^3

解答

展开

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

t^{3} + 3 e^{2 t} t^{2} + 3 e^{4 t} t + e^{6 t}

求解步骤

(t + e^{2 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 = t, b = e^{2 t}

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

化简

t^{3} + 3 t^{2} e^{2 t} + 3 t (e^{2 t})^{2} + (e^{2 t})^{3} : t^{3} + 3 e^{2 t} t^{2} + 3 e^{4 t} t + e^{6 t}

= t^{3} + 3 e^{2 t} t^{2} + 3 e^{4 t} t + e^{6 t}

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