展开 (t-e^{2t})(3+2e^{2t})

解答

展开

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

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

求解步骤

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

使用 FOIL 方法:

(a + b) (c + d) = a c + a d + b c + b d

a = t, b = - e^{2 t}, c = 3, d = 2 e^{2 t}

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

使用加减运算法则

+ (- a) = - a

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

2 e^{2 t} e^{2 t} = 2 e^{4 t}

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

e x p an d (2 t + 3) \cdot (ln (2 t - 3))

e x p an d 4 (x - 1) - 2 (3 x + 5 = - 3 x - 1)

e x p an d e^{P} (P + P P)

e x p an d \frac{( x ^{2} - 1 )}{( x - 4 ) \cdot 5}

e x p an d (w + 7) (w + 3)^{'}