展开-e^t*(2e^t+8te^t)

解答

展开

- e^{t} \cdot (2 e^{t} + 8 t e^{t})

- 2 e^{2 t} - 8 e^{2 t} t

求解步骤

- e^{t} (2 e^{t} + 8 t e^{t})

= - e^{t} (2 e^{t} + 8 e^{t} t)

使用分配律:

a (b + c) = ab + a c

a = - e^{t}, b = 2 e^{t}, c = 8 t e^{t}

= - e^{t} \cdot 2 e^{t} + (- e^{t}) \cdot 8 t e^{t}

使用加减运算法则

+ (- a) = - a

= - 2 e^{t} e^{t} - 8 e^{t} e^{t} t

化简

- 2 e^{t} e^{t} - 8 e^{t} e^{t} t : - 2 e^{2 t} - 8 e^{2 t} t

= - 2 e^{2 t} - 8 e^{2 t} t

e x p an d x y d y (y + 1) (1 - x) d x

e x p an d y (2 x^{2} - x y + y^{2}) d x

e x p an d \frac{1}{2 ( 4 x - 10 ) ( 2 x + 3 )}

e x p an d (2, 1, - 1) \cdot (1, x, 0)

e x p an d (ln (x)) (x^{3} - 16)