erweitern 1/5 (x+4)(x+1)^2(x-3)

Lösung

erweitern

\frac{1}{5} (x + 4) (x + 1)^{2} (x - 3)

\frac{x ^{4}}{5} + \frac{3 x ^{3}}{5} - \frac{9 x ^{2}}{5} - \frac{23 x}{5} - \frac{12}{5}

Schritte zur Lösung

\frac{1}{5} (x + 4) (x + 1)^{2} (x - 3)

= \frac{1}{5} (x + 1)^{2} (x + 4) (x - 3)

Schreibe

(x + 1)^{2}

um:

x^{2} + 2 x + 1

= \frac{1}{5} (x^{2} + 2 x + 1) (x + 4) (x - 3)

Apply FOIL method

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

= \frac{1}{5} (x^{2} + 2 x + 1) (x^{2} + x - 12)

Schreibe

(x^{2} + 2 x + 1) (x^{2} + x - 12)

um:

x^{4} + 3 x^{3} - 9 x^{2} - 23 x - 12

= \frac{1}{5} (x^{4} + 3 x^{3} - 9 x^{2} - 23 x - 12)

Setze Klammern

= \frac{1}{5} x^{4} + \frac{1}{5} \cdot 3 x^{3} + \frac{1}{5} (- 9 x^{2}) + \frac{1}{5} (- 23 x) + \frac{1}{5} (- 12)

Vereinfache

\frac{1}{5} x^{4} + \frac{1}{5} \cdot 3 x^{3} + \frac{1}{5} (- 9 x^{2}) + \frac{1}{5} (- 23 x) + \frac{1}{5} (- 12) : \frac{x ^{4}}{5} + \frac{3 x ^{3}}{5} - \frac{9 x ^{2}}{5} - \frac{23 x}{5} - \frac{12}{5}

= \frac{x ^{4}}{5} + \frac{3 x ^{3}}{5} - \frac{9 x ^{2}}{5} - \frac{23 x}{5} - \frac{12}{5}

e x p an d \frac{2 ( a + b ) ( a - b )}{a - b ^{2}}

s im pl i f y - 2 (- 2 sec^{2} (x) + 3 sec^{4} (x))

s im pl i f y (\frac{a}{6} - \frac{x ^{3}}{5}) (\frac{a}{6} + \frac{x ^{3}}{5})

s im pl i f y 4 (cos^{2} (2 x) + sin^{2} (2 y))

e x p an d (5 - 22) (5 + 2)