展開する (e^2sin^2(t)-3cos^2(t))(-sin(t))

解

展開する

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

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

解答ステップ

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

= (- sin (t)) (e^{2} sin^{2} (t) - 3 cos^{2} (t))

分配法則を適用する:

a (b - c) = ab - a c

a = (- sin (t)), b = e^{2} sin^{2} (t), c = 3 cos^{2} (t)

= (- sin (t)) e^{2} sin^{2} (t) - (- sin (t)) \cdot 3 cos^{2} (t)

= e^{2} (- sin (t)) sin^{2} (t) - 3 (- sin (t)) cos^{2} (t)

簡素化

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

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