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) \cdot 2 t sin (t) - sin (t) sin^{2} (t)

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

Simplify

- sin (t) t^{2} - sin (t) \cdot 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)

arctan (f (5 x^{5} + 4))

cos ((5 + n) π)

(43 - 7) (43 - 37)^{'}

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

3 x^{2} (x^{2} - 2)^{4} d x

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)