erweitern 1/12 (x+2)^2(x-3)^2

Lösung

erweitern

\frac{1}{12} (x + 2)^{2} (x - 3)^{2}

\frac{x ^{4}}{12} - \frac{x ^{3}}{6} - \frac{11 x ^{2}}{12} + x + 3

Schritte zur Lösung

\frac{1}{12} (x + 2)^{2} (x - 3)^{2}

Schreibe

(x + 2)^{2}

um:

x^{2} + 4 x + 4

= \frac{1}{12} (x^{2} + 4 x + 4) (x - 3)^{2}

= \frac{1}{12} (x - 3)^{2} (x^{2} + 4 x + 4)

Schreibe

(x - 3)^{2}

um:

x^{2} - 6 x + 9

= \frac{1}{12} (x^{2} - 6 x + 9) (x^{2} + 4 x + 4)

Schreibe

(x^{2} - 6 x + 9) (x^{2} + 4 x + 4)

um:

x^{4} - 2 x^{3} - 11 x^{2} + 12 x + 36

= \frac{1}{12} (x^{4} - 2 x^{3} - 11 x^{2} + 12 x + 36)

Setze Klammern

= \frac{1}{12} x^{4} + \frac{1}{12} (- 2 x^{3}) + \frac{1}{12} (- 11 x^{2}) + \frac{1}{12} \cdot 12 x + \frac{1}{12} \cdot 36

Vereinfache

\frac{1}{12} x^{4} + \frac{1}{12} (- 2 x^{3}) + \frac{1}{12} (- 11 x^{2}) + \frac{1}{12} \cdot 12 x + \frac{1}{12} \cdot 36 : \frac{x ^{4}}{12} - \frac{x ^{3}}{6} - \frac{11 x ^{2}}{12} + x + 3

= \frac{x ^{4}}{12} - \frac{x ^{3}}{6} - \frac{11 x ^{2}}{12} + x + 3

e x p an d (sin (2 x) sin (x) + cos (4 x) cos (x)) sec (2 x)

e x p an d - \frac{7}{( s ^{2} - 6 s + 8 ) ( s - 3 )}

s im pl i f y 11 (17 + 122)

e x p an d \frac{5 x + 13}{( x - 1 ) ( x + 5 )}

e x p an d \frac{1 - e ^{- 3 s}}{s ( s ^{2} + 2 s + 10 )}