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

Lösung

erweitern

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

- 4 x^{5} - 50 x^{4} - \frac{865 x ^{3}}{4} - 355 x^{2} - 140 x - 16

Schritte zur Lösung

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

(4 x + 1)^{2} = 16 x^{2} + 8 x + 1

= - \frac{( 16 x ^{2} + 8 x + 1 ) ( x + 4 ) ^{3}}{4}

(x + 4)^{3} = x^{3} + 12 x^{2} + 48 x + 64

= - \frac{( 16 x ^{2} + 8 x + 1 ) ( x ^{3} + 12 x ^{2} + 48 x + 64 )}{4}

Multipliziere aus

(16 x^{2} + 8 x + 1) (x^{3} + 12 x^{2} + 48 x + 64) : 16 x^{5} + 200 x^{4} + 865 x^{3} + 1420 x^{2} + 560 x + 64

= - \frac{16 x ^{5} + 200 x ^{4} + 865 x ^{3} + 1420 x ^{2} + 560 x + 64}{4}

Wende Bruchregel an:

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

\frac{16 x ^{5} + 200 x ^{4} + 865 x ^{3} + 1420 x ^{2} + 560 x + 64}{4} = - (\frac{16 x ^{5}}{4}) - (\frac{200 x ^{4}}{4}) - (\frac{865 x ^{3}}{4}) - (\frac{1420 x ^{2}}{4}) - (\frac{560 x}{4}) - (\frac{64}{4})

= - (\frac{16 x ^{5}}{4}) - (\frac{200 x ^{4}}{4}) - (\frac{865 x ^{3}}{4}) - (\frac{1420 x ^{2}}{4}) - (\frac{560 x}{4}) - (\frac{64}{4})

Entferne die Klammern:

(a) = a

= - \frac{16 x ^{5}}{4} - \frac{200 x ^{4}}{4} - \frac{865 x ^{3}}{4} - \frac{1420 x ^{2}}{4} - \frac{560 x}{4} - \frac{64}{4}

\frac{16 x ^{5}}{4} = 4 x^{5}

\frac{200 x ^{4}}{4} = 50 x^{4}

\frac{1420 x ^{2}}{4} = 355 x^{2}

\frac{560 x}{4} = 140 x

\frac{64}{4} = 16

= - 4 x^{5} - 50 x^{4} - \frac{865 x ^{3}}{4} - 355 x^{2} - 140 x - 16

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

e x p an d 1 - (- 3 + 6 + 1) - [4 - (6 - 3 + 1) = 2]

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

e x p an d \frac{4 π}{3} (r + 4)^{3}

e x p an d cos (2 (k + 1))