erweitern (x^3+3x^2+6x+4)^5

Lösung

erweitern

(x^{3} + 3 x^{2} + 6 x + 4)^{5}

x^{15} + 15 x^{14} + 120 x^{13} + 650 x^{12} + 2625 x^{11} + 8283 x^{10} + 20950 x^{9} + 43020 x^{8} + 72000 x^{7} + 97840 x^{6} + 106656 x^{5} + 91200 x^{4} + 58880 x^{3} + 26880 x^{2} + 7680 x + 1024

Schritte zur Lösung

(x^{3} + 3 x^{2} + 6 x + 4)^{5}

(x^{3} + 3 x^{2} + 6 x + 4)^{5} = (x^{3} + 3 x^{2} + 6 x + 4) (x^{3} + 3 x^{2} + 6 x + 4) (x^{3} + 3 x^{2} + 6 x + 4) (x^{3} + 3 x^{2} + 6 x + 4) (x^{3} + 3 x^{2} + 6 x + 4)

= (x^{3} + 3 x^{2} + 6 x + 4) (x^{3} + 3 x^{2} + 6 x + 4) (x^{3} + 3 x^{2} + 6 x + 4) (x^{3} + 3 x^{2} + 6 x + 4) (x^{3} + 3 x^{2} + 6 x + 4)

Multipliziere aus

(x^{3} + 3 x^{2} + 6 x + 4) (x^{3} + 3 x^{2} + 6 x + 4) (x^{3} + 3 x^{2} + 6 x + 4) (x^{3} + 3 x^{2} + 6 x + 4) (x^{3} + 3 x^{2} + 6 x + 4) : x^{15} + 15 x^{14} + 120 x^{13} + 650 x^{12} + 2625 x^{11} + 8283 x^{10} + 20950 x^{9} + 43020 x^{8} + 72000 x^{7} + 97840 x^{6} + 106656 x^{5} + 91200 x^{4} + 58880 x^{3} + 26880 x^{2} + 7680 x + 1024

= x^{15} + 15 x^{14} + 120 x^{13} + 650 x^{12} + 2625 x^{11} + 8283 x^{10} + 20950 x^{9} + 43020 x^{8} + 72000 x^{7} + 97840 x^{6} + 106656 x^{5} + 91200 x^{4} + 58880 x^{3} + 26880 x^{2} + 7680 x + 1024

e x p an d tan (h) (x + y)

\frac{d}{d q} ((R (q)) (q^{4} + 1)^{7})

e x p an d \frac{3 x}{( x - 8 ) ( x + 5 )}

s im pl i f y (\frac{9}{x - 14} + 7 (100 - x)) (x - 14)

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