展开 e^{2t}(t-1)^2

解答

展开

e^{2 t} (t - 1)^{2}

e^{2 t} t^{2} - 2 e^{2 t} t + e^{2 t}

求解步骤

e^{2 t} (t - 1)^{2}

(t - 1)^{2} = t^{2} - 2 t + 1

= e^{2 t} (t^{2} - 2 t + 1)

打开括号

= e^{2 t} t^{2} + e^{2 t} (- 2 t) + e^{2 t} \cdot 1

使用加减运算法则

+ (- a) = - a

= e^{2 t} t^{2} - 2 e^{2 t} t + 1 \cdot e^{2 t}

乘以:

1 \cdot e^{2 t} = e^{2 t}

= e^{2 t} t^{2} - 2 e^{2 t} t + e^{2 t}

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