展開する-sin(t)(t+sin(t))^2

解

展開する

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

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

解答ステップ

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

拡張

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

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

分配法則を適用する:

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)

簡素化

- 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)