展开 (x+sin(x)-1)^2

解答

展开

(x + sin (x) - 1)^{2}

- 2 sin (x) + x^{2} + sin^{2} (x) + 2 x sin (x) - 2 x + 1

求解步骤

(x + sin (x) - 1)^{2}

使用指数法则:

a^{b + c} = a^{b} \cdot a^{c}

(x + sin (x) - 1)^{2} = (x + sin (x) - 1) (x + sin (x) - 1)

= (x + sin (x) - 1) (x + sin (x) - 1)

打开括号

= xx + x sin (x) + x (- 1) + sin (x) x + sin (x) sin (x) + sin (x) (- 1) - 1 \cdot x - 1 \cdot sin (x) - 1 \cdot (- 1)

化简

xx + x sin (x) + x (- 1) + sin (x) x + sin (x) sin (x) + sin (x) (- 1) - 1 \cdot x - 1 \cdot sin (x) - 1 \cdot (- 1) : - 2 sin (x) + x^{2} + sin^{2} (x) + 2 x sin (x) - 2 x + 1

= - 2 sin (x) + x^{2} + sin^{2} (x) + 2 x sin (x) - 2 x + 1

e x p an d (2 x) (3 x + 1 + 1)

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

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

e x p an d sin (\frac{( 2 x - 1 ) π}{2})

s im pl i f y 0.502348 (- cos (θ) + 1)