erweitern (2+x+x^4)(5x-1/(2x^3))^8

Lösung

erweitern

(2 + x + x^{4}) (5 x - \frac{1}{2 x ^{3}})^{8}

\frac{( 10 x ^{4} - 1 ) ^{8}}{128 x ^{24}} + \frac{( 10 x ^{4} - 1 ) ^{8}}{256 x ^{23}} + \frac{( 10 x ^{4} - 1 ) ^{8}}{256 x ^{20}}

Schritte zur Lösung

(2 + x + x^{4}) (5 x - \frac{1}{2 x ^{3}})^{8}

= (5 x - \frac{1}{2 x ^{3}})^{8} (2 + x + x^{4})

Wende das Distributivgesetz an:

m (a + b + c) = ma + mb + m c

(5 x - \frac{1}{2 x ^{3}})^{8} (2 + x + x^{4}) = (5 x - \frac{1}{2 x ^{3}})^{8} \cdot 2 + (5 x - \frac{1}{2 x ^{3}})^{8} x + (5 x - \frac{1}{2 x ^{3}})^{8} x^{4}

= (5 x - \frac{1}{2 x ^{3}})^{8} \cdot 2 + (5 x - \frac{1}{2 x ^{3}})^{8} x + (5 x - \frac{1}{2 x ^{3}})^{8} x^{4}

Vereinfache

(5 x - \frac{1}{2 x ^{3}})^{8} \cdot 2 + (5 x - \frac{1}{2 x ^{3}})^{8} x + (5 x - \frac{1}{2 x ^{3}})^{8} x^{4} : \frac{( 10 x ^{4} - 1 ) ^{8}}{128 x ^{24}} + \frac{( 10 x ^{4} - 1 ) ^{8}}{256 x ^{23}} + \frac{( 10 x ^{4} - 1 ) ^{8}}{256 x ^{20}}

= \frac{( 10 x ^{4} - 1 ) ^{8}}{128 x ^{24}} + \frac{( 10 x ^{4} - 1 ) ^{8}}{256 x ^{23}} + \frac{( 10 x ^{4} - 1 ) ^{8}}{256 x ^{20}}

e x p an d A (- 4, - 5) B (- 2, 3) C (1, - 2)

e x p an d \frac{( 3 x - 1 ) ^{2}}{9}

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

s im pl i f y 10 (lo g_{10} (2) + 7)

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