erweitern (a+b*cos(t))^3

Lösung

erweitern

(a + b \cdot cos (t))^{3}

a^{3} + 3 a^{2} b cos (t) + 3 a b^{2} cos^{2} (t) + b^{3} cos^{3} (t)

Schritte zur Lösung

(a + b cos (t))^{3}

Wende Formel für perfekte dritte Potenzen an:

(a + b)^{3} = a^{3} + 3 a^{2} b + 3 a b^{2} + b^{3}

(a + b cos (t))^{3} = a^{3} + 3 a^{2} b cos (t) + 3 a (b cos (t))^{2} + (b cos (t))^{3}

= a^{3} + 3 a^{2} b cos (t) + 3 a (b cos (t))^{2} + (b cos (t))^{3}

Vereinfache

a^{3} + 3 a^{2} b cos (t) + 3 a (b cos (t))^{2} + (b cos (t))^{3} : a^{3} + 3 a^{2} b cos (t) + 3 a b^{2} cos^{2} (t) + b^{3} cos^{3} (t)

= a^{3} + 3 a^{2} b cos (t) + 3 a b^{2} cos^{2} (t) + b^{3} cos^{3} (t)

s im pl i f y 95 (1 + 3)

e x p an d (x + y = 1, 2) (x - 2 y = 16)

e x p an d (t^{\frac{1}{2}} + 6) (t + 9)

e x p an d (2 5 - 3) \cdot (25 - 7)

e x p an d (1 + 0.003 e^{0.8 t})^{2}