erweitern (d^2e^3f^4-3)(d^2e^3f^4+5)

Lösung

erweitern

(d^{2} e^{3} f^{4} - 3) (d^{2} e^{3} f^{4} + 5)

e^{6} d^{4} f^{8} + 2 e^{3} d^{2} f^{4} - 15

Schritte zur Lösung

(d^{2} e^{3} f^{4} - 3) (d^{2} e^{3} f^{4} + 5)

= (e^{3} d^{2} f^{4} - 3) (e^{3} d^{2} f^{4} + 5)

Wende Ausklammerungsregel an (VANI):

(a + b) (c + d) = a c + a d + b c + b d

a = d^{2} e^{3} f^{4}, b = - 3, c = d^{2} e^{3} f^{4}, d = 5

= d^{2} e^{3} f^{4} d^{2} e^{3} f^{4} + d^{2} e^{3} f^{4} \cdot 5 + (- 3) d^{2} e^{3} f^{4} + (- 3) \cdot 5

Wende Minus-Plus Regeln an

+ (- a) = - a

= e^{3} e^{3} d^{2} d^{2} f^{4} f^{4} + 5 e^{3} d^{2} f^{4} - 3 e^{3} d^{2} f^{4} - 3 \cdot 5

Vereinfache

e^{3} e^{3} d^{2} d^{2} f^{4} f^{4} + 5 e^{3} d^{2} f^{4} - 3 e^{3} d^{2} f^{4} - 3 \cdot 5 : e^{6} d^{4} f^{8} + 2 e^{3} d^{2} f^{4} - 15

= e^{6} d^{4} f^{8} + 2 e^{3} d^{2} f^{4} - 15

e x p an d e^{t - 2} h (t - 2)

s im pl i f y (x - 2) (x - 2)

e x p an d - \frac{s}{2 ( s ^{2} + 8 s + 16 )}

e x p an d 4.9 (5 - \frac{s}{340})^{2}

d o main f (x) = (e^{x} + e^{- x})^{4}