erweitern x^{4/5}(9x-36)^2

Lösung

erweitern

x^{\frac{4}{5}} (9 x - 36)^{2}

81 x^{\frac{14}{5}} - 648 x^{\frac{9}{5}} + x^{\frac{4}{5}} \cdot 1296

Schritte zur Lösung

x^{\frac{4}{5}} (9 x - 36)^{2}

Schreibe

(9 x - 36)^{2}

um:

81 x^{2} - 648 x + 1296

= x^{\frac{4}{5}} (81 x^{2} - 648 x + 1296)

Wende das Distributivgesetz an:

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

x^{\frac{4}{5}} (81 x^{2} - 648 x + 1296) = x^{\frac{4}{5}} \cdot 81 x^{2} + x^{\frac{4}{5}} (- 648 x) + x^{\frac{4}{5}} \cdot 1296

= x^{\frac{4}{5}} \cdot 81 x^{2} + x^{\frac{4}{5}} (- 648 x) + x^{\frac{4}{5}} \cdot 1296

x^{\frac{4}{5}} \cdot 81 x^{2} = 81 x^{\frac{14}{5}}

x^{\frac{4}{5}} (- 648 x) = - 648 x^{\frac{9}{5}}

= 81 x^{\frac{14}{5}} - 648 x^{\frac{9}{5}} + x^{\frac{4}{5}} \cdot 1296

e x p an d y^{''} (x) - (x + 1) y^{'} (x) - y

e x p an d \frac{( 4 x ^{4} - 1 ) ^{2}}{16 x ^{4}}

s im pl i f y (a + b)^{2}

s im pl i f y (2 + 4 - x)^{2}

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