erweitern 4(1+cos(3x^2))^4

Lösung

erweitern

4 (1 + cos (3 x^{2}))^{4}

4 + 16 cos (3 x^{2}) + 24 cos^{2} (3 x^{2}) + 16 cos^{3} (3 x^{2}) + 4 cos^{4} (3 x^{2})

Schritte zur Lösung

4 (1 + cos (3 x^{2}))^{4}

Schreibe

(1 + cos (3 x^{2}))^{4}

um:

1 + 4 cos (3 x^{2}) + 6 cos^{2} (3 x^{2}) + 4 cos^{3} (3 x^{2}) + cos^{4} (3 x^{2})

= 4 (1 + 4 cos (3 x^{2}) + 6 cos^{2} (3 x^{2}) + 4 cos^{3} (3 x^{2}) + cos^{4} (3 x^{2}))

Setze Klammern

= 4 \cdot 1 + 4 \cdot 4 cos (3 x^{2}) + 4 \cdot 6 cos^{2} (3 x^{2}) + 4 \cdot 4 cos^{3} (3 x^{2}) + 4 cos^{4} (3 x^{2})

Vereinfache

4 \cdot 1 + 4 \cdot 4 cos (3 x^{2}) + 4 \cdot 6 cos^{2} (3 x^{2}) + 4 \cdot 4 cos^{3} (3 x^{2}) + 4 cos^{4} (3 x^{2}) : 4 + 16 cos (3 x^{2}) + 24 cos^{2} (3 x^{2}) + 16 cos^{3} (3 x^{2}) + 4 cos^{4} (3 x^{2})

= 4 + 16 cos (3 x^{2}) + 24 cos^{2} (3 x^{2}) + 16 cos^{3} (3 x^{2}) + 4 cos^{4} (3 x^{2})

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

e x p an d \frac{1}{( 3 x + 1 ) ^{2}}

e x p an d \frac{d x}{( x + 2 ) ( x ^{2} + 2 x + 4 ) ^{2}}

e x p an d - \frac{1}{( x - 5 ) ^{2}}

e x p an d - \frac{1.2 ( 1 - 0.03 x ^{2} )}{( 0.01 x ^{2} + 1 ) ^{3}}