erweitern ((2+x)/((10x^2-1)))(1000x^6-1)

Lösung

erweitern

(\frac{2 + x}{( 10 x ^{2} - 1 )}) (1000 x^{6} - 1)

100 x^{5} + 10 x^{3} + x + 200 x^{4} + 20 x^{2} + 2

Schritte zur Lösung

(\frac{2 + x}{10 x ^{2} - 1}) (1000 x^{6} - 1)

Apply rule:

(a) = a

(\frac{2 + x}{10 x ^{2} - 1}) = \frac{2 + x}{10 x ^{2} - 1}

= \frac{2 + x}{10 x ^{2} - 1} (1000 x^{6} - 1)

Wende das Distributivgesetz an:

a (b - c) = ab - a c

\frac{2 + x}{10 x ^{2} - 1} (1000 x^{6} - 1) = \frac{2 + x}{10 x ^{2} - 1} \cdot 1000 x^{6} - \frac{2 + x}{10 x ^{2} - 1} \cdot 1

= \frac{2 + x}{10 x ^{2} - 1} \cdot 1000 x^{6} - \frac{2 + x}{10 x ^{2} - 1} \cdot 1

Vereinfache

\frac{2 + x}{10 x ^{2} - 1} \cdot 1000 x^{6} - \frac{2 + x}{10 x ^{2} - 1} \cdot 1 : 100 x^{5} + 10 x^{3} + x + 200 x^{4} + 20 x^{2} + 2

= 100 x^{5} + 10 x^{3} + x + 200 x^{4} + 20 x^{2} + 2

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