erweitern (x^3+2x+1)^5

Lösung

erweitern

(x^{3} + 2 x + 1)^{5}

x^{15} + 10 x^{13} + 5 x^{12} + 40 x^{11} + 40 x^{10} + 90 x^{9} + 120 x^{8} + 140 x^{7} + 170 x^{6} + 152 x^{5} + 120 x^{4} + 85 x^{3} + 40 x^{2} + 10 x + 1

Schritte zur Lösung

(x^{3} + 2 x + 1)^{5}

(x^{3} + 2 x + 1)^{5} = (x^{3} + 2 x + 1) (x^{3} + 2 x + 1) (x^{3} + 2 x + 1) (x^{3} + 2 x + 1) (x^{3} + 2 x + 1)

= (x^{3} + 2 x + 1) (x^{3} + 2 x + 1) (x^{3} + 2 x + 1) (x^{3} + 2 x + 1) (x^{3} + 2 x + 1)

Multipliziere aus

(x^{3} + 2 x + 1) (x^{3} + 2 x + 1) (x^{3} + 2 x + 1) (x^{3} + 2 x + 1) (x^{3} + 2 x + 1) : x^{15} + 10 x^{13} + 5 x^{12} + 40 x^{11} + 40 x^{10} + 90 x^{9} + 120 x^{8} + 140 x^{7} + 170 x^{6} + 152 x^{5} + 120 x^{4} + 85 x^{3} + 40 x^{2} + 10 x + 1

= x^{15} + 10 x^{13} + 5 x^{12} + 40 x^{11} + 40 x^{10} + 90 x^{9} + 120 x^{8} + 140 x^{7} + 170 x^{6} + 152 x^{5} + 120 x^{4} + 85 x^{3} + 40 x^{2} + 10 x + 1

e x p an d (3 x^{2} + y) d x

e x p an d \frac{( a - 4 ) ( a + 6 )}{6}

e x p an d \frac{2 ( 3 + 4 z )}{3 w - 4 z}

e x p an d 3 x^{2} + x^{2}

e x p an d a \cdot ((a - b) \cdot (a + 2 b))