展开 (e^t+at-2)(t^3-2t^2+1)

解答

展开

(e^{t} + a t - 2) (t^{3} - 2 t^{2} + 1)

e^{t} t^{3} - 2 e^{t} t^{2} + e^{t} + t^{4} a - 2 t^{3} a + t a - 2 t^{3} + 4 t^{2} - 2

求解步骤

(e^{t} + a t - 2) (t^{3} - 2 t^{2} + 1)

= (e^{t} + t a - 2) (t^{3} - 2 t^{2} + 1)

打开括号

= e^{t} t^{3} + e^{t} (- 2 t^{2}) + e^{t} \cdot 1 + a t t^{3} + a t (- 2 t^{2}) + a t \cdot 1 + (- 2) t^{3} + (- 2) (- 2 t^{2}) + (- 2) \cdot 1

使用加减运算法则

+ (- a) = - a, (- a) (- b) = ab

= e^{t} t^{3} - 2 e^{t} t^{2} + 1 \cdot e^{t} + t^{3} t a - 2 t^{2} t a + 1 \cdot t a - 2 t^{3} + 2 \cdot 2 t^{2} - 2 \cdot 1

化简

e^{t} t^{3} - 2 e^{t} t^{2} + 1 \cdot e^{t} + t^{3} t a - 2 t^{2} t a + 1 \cdot t a - 2 t^{3} + 2 \cdot 2 t^{2} - 2 \cdot 1 : e^{t} t^{3} - 2 e^{t} t^{2} + e^{t} + t^{4} a - 2 t^{3} a + t a - 2 t^{3} + 4 t^{2} - 2

= e^{t} t^{3} - 2 e^{t} t^{2} + e^{t} + t^{4} a - 2 t^{3} a + t a - 2 t^{3} + 4 t^{2} - 2

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