What is expand-sin(t)(-t+sin(t))^2 ?

The solution to expand-sin(t)(-t+sin(t))^2 is -t^2sin(t)+2tsin^2(t)-sin^3(t)

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expand-sin(t)(-t+sin(t))^2

expand

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

- t^{2} sin (t) + 2 t sin^{2} (t) - sin^{3} (t)

Solution steps

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

Expand

(- t + sin (t))^{2} : t^{2} - 2 t sin (t) + sin^{2} (t)

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

Apply the distributive law:

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

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

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

Simplify

- sin (t) t^{2} - sin (t) (- 2 t sin (t)) - sin (t) sin^{2} (t) : - t^{2} sin (t) + 2 t sin^{2} (t) - sin^{3} (t)

= - t^{2} sin (t) + 2 t sin^{2} (t) - sin^{3} (t)

\frac{10 ( h + 3 )}{h - 3}

3 (x^{2} + 2 y)^{2} (2 x + 2 y^{'} (x))

x (v^{2} - 1) d v + v^{3} - 3 v

\frac{x ^{2} - 1}{( x - 2 ) ^{2}}

(a + b x + c x^{2}) \cdot (d + e x + f x^{2})

What is expand-sin(t)(-t+sin(t))^2 ?
The solution to expand-sin(t)(-t+sin(t))^2 is -t^2sin(t)+2tsin^2(t)-sin^3(t)