erweitern (D^2-D)(e^3x+3x^3)

Lösung

erweitern

(D^{2} - D) (e^{3} x + 3 x^{3})

e^{3} D^{2} x + 3 D^{2} x^{3} - e^{3} D x - 3 D x^{3}

Schritte zur Lösung

(D^{2} - D) (e^{3} x + 3 x^{3})

Wende Ausklammerungsregel an (VANI):

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

a = D^{2}, b = - D, c = e^{3} x, d = 3 x^{3}

= D^{2} e^{3} x + D^{2} \cdot 3 x^{3} + (- D) e^{3} x + (- D) \cdot 3 x^{3}

Wende Minus-Plus Regeln an

+ (- a) = - a

= e^{3} D^{2} x + 3 D^{2} x^{3} - e^{3} D x - 3 D x^{3}

e x p an d in t er sec (t) o (- 4) (x - 3)^{2} + 10

e x p an d (a + b = 1,) - (2 a + b = 5)

e x p an d \frac{( 20 d - a t ) ^{2}}{25 t ^{2}}

e x p an d \frac{( - 5 + x ) ( 5 + x )}{4 + 5 x}

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