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

Lösung

erweitern

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

x^{5} + 2 x^{4} + 3 x^{3} + 2 x^{2} + x

Schritte zur Lösung

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

(x^{2} + x + 1)^{2} = x^{4} + 2 x^{3} + 3 x^{2} + 2 x + 1

= x (x^{4} + 2 x^{3} + 3 x^{2} + 2 x + 1)

Setze Klammern

= x x^{4} + x \cdot 2 x^{3} + x \cdot 3 x^{2} + x \cdot 2 x + x \cdot 1

= x^{4} x + 2 x^{3} x + 3 x^{2} x + 2 xx + 1 \cdot x

Vereinfache

x^{4} x + 2 x^{3} x + 3 x^{2} x + 2 xx + 1 \cdot x : x^{5} + 2 x^{4} + 3 x^{3} + 2 x^{2} + x

= x^{5} + 2 x^{4} + 3 x^{3} + 2 x^{2} + x

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

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

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

e x p an d u (t - π) cos (t)