展开 (10e^t+2)(t^4+1)

解答

展开

(10 e^{t} + 2) (t^{4} + 1)

10 e^{t} t^{4} + 10 e^{t} + 2 t^{4} + 2

求解步骤

(10 e^{t} + 2) (t^{4} + 1)

使用 FOIL 方法:

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

a = 10 e^{t}, b = 2, c = t^{4}, d = 1

= 10 e^{t} t^{4} + 10 e^{t} \cdot 1 + 2 t^{4} + 2 \cdot 1

= 10 e^{t} t^{4} + 10 \cdot 1 \cdot e^{t} + 2 t^{4} + 2 \cdot 1

化简

10 e^{t} t^{4} + 10 \cdot 1 \cdot e^{t} + 2 t^{4} + 2 \cdot 1 : 10 e^{t} t^{4} + 10 e^{t} + 2 t^{4} + 2

= 10 e^{t} t^{4} + 10 e^{t} + 2 t^{4} + 2

e x p an d \frac{( x + 1 ) ( x - 5 )}{( x + 5 ) ( x - 1 )}

e x p an d \frac{4}{( s - 2 ) ( s ^{2} - 4 s - 4 )}

e x p an d (0.25 + 0.75 e^{t})^{5}

e x p an d \frac{( x + 1 ) y}{x}

e x p an d (- 2, - 6) y (12, 18)