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

The solution to expand (sin(x)-1)^2(sin(x)+1) is sin^3(x)+cos^2(x)-sin(x)

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

expand

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

sin^{3} (x) + cos^{2} (x) - sin (x)

Solution steps

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

Expand

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

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

Distribute parentheses

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

Simplify

sin^{2} (x) sin (x) + sin^{2} (x) \cdot 1 - 2 sin (x) sin (x) - 2 sin (x) \cdot 1 + 1 \cdot sin (x) + 1 \cdot 1 : sin^{3} (x) + cos^{2} (x) - sin (x)

= sin^{3} (x) + cos^{2} (x) - sin (x)

- 2 l e f t (1 + x^{2})^{2}

\frac{d}{d θ} ((x (θ)) a (θ - sin (θ)))

(cos (t) + i sin (t))^{2} (- sin (t) + i cos (t))

\frac{1}{3} (- t^{3} + 2 - cot (t^{3} - 2))

sin (t) - y e^{t} (- t e^{- t} - e^{- t} + 1)

What is expand (sin(x)-1)^2(sin(x)+1) ?
The solution to expand (sin(x)-1)^2(sin(x)+1) is sin^3(x)+cos^2(x)-sin(x)