erweitern ((x+1)^2(x+2)^2)/4

Lösung

erweitern

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

\frac{x ^{4}}{4} + \frac{3 x ^{3}}{2} + \frac{13 x ^{2}}{4} + 3 x + 1

Schritte zur Lösung

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

(x + 1)^{2} = x^{2} + 2 x + 1

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

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

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

Multipliziere aus

(x^{2} + 2 x + 1) (x^{2} + 4 x + 4) : x^{4} + 6 x^{3} + 13 x^{2} + 12 x + 4

= \frac{x ^{4} + 6 x ^{3} + 13 x ^{2} + 12 x + 4}{4}

Wende Bruchregel an:

\frac{a \pm b}{c} = \frac{a}{c} \pm \frac{b}{c}

\frac{x ^{4} + 6 x ^{3} + 13 x ^{2} + 12 x + 4}{4} = \frac{x ^{4}}{4} + \frac{6 x ^{3}}{4} + \frac{13 x ^{2}}{4} + \frac{12 x}{4} + \frac{4}{4}

= \frac{x ^{4}}{4} + \frac{6 x ^{3}}{4} + \frac{13 x ^{2}}{4} + \frac{12 x}{4} + \frac{4}{4}

Wende Regel an

\frac{a}{a} = 1

\frac{4}{4} = 1

= \frac{x ^{4}}{4} + \frac{6 x ^{3}}{4} + \frac{13 x ^{2}}{4} + \frac{12 x}{4} + 1

Streiche

\frac{6 x ^{3}}{4} : \frac{3 x ^{3}}{2}

= \frac{x ^{4}}{4} + \frac{3 x ^{3}}{2} + \frac{13 x ^{2}}{4} + \frac{12 x}{4} + 1

Teile die Zahlen:

\frac{12}{4} = 3

= \frac{x ^{4}}{4} + \frac{3 x ^{3}}{2} + \frac{13 x ^{2}}{4} + 3 x + 1

e x p an d cos (x) d x + (1 + \frac{2}{y}) sin (x) d y

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

s im pl i f y (cos (A) + 1) (cos (A) - 1)

e x p an d \frac{1}{( 1 - x ) ( 2 - x )}

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