erweitern (x+1)(x-2)(x+3)(x+4)

Lösung

erweitern

(x + 1) (x - 2) (x + 3) (x + 4)

x^{4} + 6 x^{3} + 3 x^{2} - 26 x - 24

Schritte zur Lösung

(x + 1) (x - 2) (x + 3) (x + 4)

Schreibe

(x + 1) (x - 2) (x + 3) (x + 4)

um:

(x^{2} - x - 2) (x + 3) (x + 4)

= (x^{2} - x - 2) (x + 3) (x + 4)

Apply FOIL method

(x + 3) (x + 4) : x^{2} + 7 x + 12

= (x^{2} - x - 2) (x^{2} + 7 x + 12)

Setze Klammern

= x^{2} x^{2} + x^{2} \cdot 7 x + x^{2} \cdot 12 - x x^{2} - x \cdot 7 x - x \cdot 12 - 2 x^{2} - 2 \cdot 7 x - 2 \cdot 12

Vereinfache

x^{2} x^{2} + x^{2} \cdot 7 x + x^{2} \cdot 12 - x x^{2} - x \cdot 7 x - x \cdot 12 - 2 x^{2} - 2 \cdot 7 x - 2 \cdot 12 : x^{4} + 6 x^{3} + 3 x^{2} - 26 x - 24

= x^{4} + 6 x^{3} + 3 x^{2} - 26 x - 24

s im pl i f y \frac{( a ^{\frac{5}{3}} )}{y ^{4} x ^{2}}

\frac{a}{6} = 5

s im pl i f y - 5 \cdot 2

s im pl i f y \frac{- 1 + 2 i}{i}

3 x^{2} + 4 x + 1 = 0