展开 (2t-5)^2sin(t)

解答

展开

(2 t - 5)^{2} sin (t)

4 t^{2} sin (t) - 20 t sin (t) + 25 sin (t)

求解步骤

(2 t - 5)^{2} sin (t)

= sin (t) (2 t - 5)^{2}

展开

(2 t - 5)^{2} : 4 t^{2} - 20 t + 25

= sin (t) (4 t^{2} - 20 t + 25)

使用分配律:

m (a + b + c) = ma + mb + m c

sin (t) (4 t^{2} - 20 t + 25) = sin (t) \cdot 4 t^{2} + sin (t) (- 20 t) + sin (t) \cdot 25

= sin (t) \cdot 4 t^{2} + sin (t) (- 20 t) + sin (t) \cdot 25

化简

sin (t) \cdot 4 t^{2} + sin (t) (- 20 t) + sin (t) \cdot 25 : 4 t^{2} sin (t) - 20 t sin (t) + 25 sin (t)

= 4 t^{2} sin (t) - 20 t sin (t) + 25 sin (t)

e x p an d (3 x - 3) \cdot (3 x + 3)^{3}

e x p an d (u - 1) u^{\frac{1}{2}}

e x p an d (2 x + 9 - x)^{2}

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

e x p an d 4 xv d v + (3 v^{2} - 1) d x