erweitern (a+c-cos(x)b)^2

Lösung

erweitern

(a + c - cos (x) b)^{2}

a^{2} + 2 a c - 2 ab cos (x) + c^{2} + cos^{2} (x) b^{2} - 2 c b cos (x)

Schritte zur Lösung

(a + c - cos (x) b)^{2}

Wende Exponentenregel an:

a^{b + c} = a^{b} \cdot a^{c}

(a + c - cos (x) b)^{2} = (a + c - cos (x) b) (a + c - cos (x) b)

= (a + c - cos (x) b) (a + c - cos (x) b)

Setze Klammern

= aa + a c + a (- cos (x) b) + c a + cc + c (- cos (x) b) - cos (x) ba - cos (x) b c - cos (x) b (- cos (x) b)

Vereinfache

aa + a c + a (- cos (x) b) + c a + cc + c (- cos (x) b) - cos (x) ba - cos (x) b c - cos (x) b (- cos (x) b) : a^{2} + 2 a c - 2 ab cos (x) + c^{2} + cos^{2} (x) b^{2} - 2 c b cos (x)

= a^{2} + 2 a c - 2 ab cos (x) + c^{2} + cos^{2} (x) b^{2} - 2 c b cos (x)

e x p an d \frac{2}{( s + 2 ) ^{2}}

e x p an d 5 + 1 (A cos (4 i x) + B, (4 i x))

e x p an d \frac{2 x + 3}{( x - 6 ) ( x - 3 )}

e x p an d (- e^{3 t} + 3 e^{t} - 2) (1.5 e^{- 3 t} - 1.5 e^{- t})

e x p an d (e^{3 x}) (x + C e^{- x} + C e^{- 3 x})