What is expand (x+sin(x)-1)^2 ?

The solution to expand (x+sin(x)-1)^2 is -2sin(x)+x^2+sin^2(x)+2xsin(x)-2x+1

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expand (x+sin(x)-1)^2

expand

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

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

Solution steps

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

Apply exponent rule:

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)

Distribute parentheses

= 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)

Simplify

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

(2 x) (3 x + 1 + 1)

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

\frac{3}{( s + 1 ) ( s + 2 ) ^{2}}

sin (\frac{( 2 x - 1 ) π}{2})

0.502348 (- cos (θ) + 1)

What is expand (x+sin(x)-1)^2 ?
The solution to expand (x+sin(x)-1)^2 is -2sin(x)+x^2+sin^2(x)+2xsin(x)-2x+1