erweitern (acos(w)+1+bcos(2*w))^2

Lösung

erweitern

(a \cdot cos (w) + 1 + b \cdot cos (2 \cdot w))^{2}

a^{2} cos^{2} (w) + 2 a cos (w) + 2 b cos (2 w) + b^{2} cos^{2} (2 w) + ab cos (w) cos (2 w) + ab cos (2 w) cos (w) + 1

Schritte zur Lösung

(a cos (w) + 1 + b cos (2 w))^{2}

Wende Exponentenregel an:

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

(a cos (w) + 1 + b cos (2 w))^{2} = (a cos (w) + 1 + b cos (2 w)) (a cos (w) + 1 + b cos (2 w))

= (a cos (w) + 1 + b cos (2 w)) (a cos (w) + 1 + b cos (2 w))

Setze Klammern

= a cos (w) a cos (w) + a cos (w) \cdot 1 + a cos (w) b cos (2 w) + 1 \cdot a cos (w) + 1 \cdot 1 + 1 \cdot b cos (2 w) + b cos (2 w) a cos (w) + b cos (2 w) \cdot 1 + b cos (2 w) b cos (2 w)

Vereinfache

a cos (w) a cos (w) + a cos (w) \cdot 1 + a cos (w) b cos (2 w) + 1 \cdot a cos (w) + 1 \cdot 1 + 1 \cdot b cos (2 w) + b cos (2 w) a cos (w) + b cos (2 w) \cdot 1 + b cos (2 w) b cos (2 w) : a^{2} cos^{2} (w) + 2 a cos (w) + 2 b cos (2 w) + b^{2} cos^{2} (2 w) + ab cos (w) cos (2 w) + ab cos (2 w) cos (w) + 1

= a^{2} cos^{2} (w) + 2 a cos (w) + 2 b cos (2 w) + b^{2} cos^{2} (2 w) + ab cos (w) cos (2 w) + ab cos (2 w) cos (w) + 1

e x p an d sin (b) (sec (b) + cot (b))

e x p an d (1 + x) 3 (2 x - 1)

e x p an d 2 (5 + 6)

s im pl i f y (x - 3) (x + 1) (x - \frac{1}{2}) (x - 5)

e x p an d (6 x^{6} - x^{2} y) + (- x^{3} + x^{2} y^{2}) y^{'} (x)