erweitern 5(x^2+x+1)^4

Lösung

erweitern

5 (x^{2} + x + 1)^{4}

5 x^{8} + 20 x^{7} + 50 x^{6} + 80 x^{5} + 95 x^{4} + 80 x^{3} + 50 x^{2} + 20 x + 5

Schritte zur Lösung

5 (x^{2} + x + 1)^{4}

(x^{2} + x + 1)^{4} = x^{8} + 4 x^{7} + 10 x^{6} + 16 x^{5} + 19 x^{4} + 16 x^{3} + 10 x^{2} + 4 x + 1

= 5 (x^{8} + 4 x^{7} + 10 x^{6} + 16 x^{5} + 19 x^{4} + 16 x^{3} + 10 x^{2} + 4 x + 1)

Setze Klammern

= 5 x^{8} + 5 \cdot 4 x^{7} + 5 \cdot 10 x^{6} + 5 \cdot 16 x^{5} + 5 \cdot 19 x^{4} + 5 \cdot 16 x^{3} + 5 \cdot 10 x^{2} + 5 \cdot 4 x + 5 \cdot 1

Vereinfache

5 x^{8} + 5 \cdot 4 x^{7} + 5 \cdot 10 x^{6} + 5 \cdot 16 x^{5} + 5 \cdot 19 x^{4} + 5 \cdot 16 x^{3} + 5 \cdot 10 x^{2} + 5 \cdot 4 x + 5 \cdot 1 : 5 x^{8} + 20 x^{7} + 50 x^{6} + 80 x^{5} + 95 x^{4} + 80 x^{3} + 50 x^{2} + 20 x + 5

= 5 x^{8} + 20 x^{7} + 50 x^{6} + 80 x^{5} + 95 x^{4} + 80 x^{3} + 50 x^{2} + 20 x + 5

e x p an d 3 (- 15)

e x p an d 7 (2 e - 1)

e x p an d \frac{g ( x ^{2} + 1 )}{5 x - 7}

e x p an d (a + b x) (c + d x + e x^{2})

e x p an d \frac{1}{( - 3 - 3 x ) ^{4}}