erweitern (x+x^2+x^3)^3

Lösung

erweitern

(x + x^{2} + x^{3})^{3}

x^{9} + 3 x^{8} + 6 x^{7} + 7 x^{6} + 6 x^{5} + 3 x^{4} + x^{3}

Schritte zur Lösung

(x + x^{2} + x^{3})^{3}

Vereinfache

(x + x^{2} + x^{3})^{3} : (x + x^{2} + x^{3}) (x + x^{2} + x^{3}) (x + x^{2} + x^{3})

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

Schreibe

(x + x^{2} + x^{3}) (x + x^{2} + x^{3})

um:

x^{6} + 2 x^{5} + 3 x^{4} + 2 x^{3} + x^{2}

= (x^{6} + 2 x^{5} + 3 x^{4} + 2 x^{3} + x^{2}) (x + x^{2} + x^{3})

Setze Klammern

= x^{6} x + x^{6} x^{2} + x^{6} x^{3} + 2 x^{5} x + 2 x^{5} x^{2} + 2 x^{5} x^{3} + 3 x^{4} x + 3 x^{4} x^{2} + 3 x^{4} x^{3} + 2 x^{3} x + 2 x^{3} x^{2} + 2 x^{3} x^{3} + x^{2} x + x^{2} x^{2} + x^{2} x^{3}

Vereinfache

x^{6} x + x^{6} x^{2} + x^{6} x^{3} + 2 x^{5} x + 2 x^{5} x^{2} + 2 x^{5} x^{3} + 3 x^{4} x + 3 x^{4} x^{2} + 3 x^{4} x^{3} + 2 x^{3} x + 2 x^{3} x^{2} + 2 x^{3} x^{3} + x^{2} x + x^{2} x^{2} + x^{2} x^{3} : x^{9} + 3 x^{8} + 6 x^{7} + 7 x^{6} + 6 x^{5} + 3 x^{4} + x^{3}

= x^{9} + 3 x^{8} + 6 x^{7} + 7 x^{6} + 6 x^{5} + 3 x^{4} + x^{3}

s im pl i f y \frac{v}{( x ^{2} \cdot y ^{3} )} + \frac{u}{x} - w

f a c t or 12 x^{4} + 24 x^{3} y - 36 x^{2} y^{2}

s im pl i f y (3 a + 4 a)^{2} + (3 a - 4 a)^{2}

f a c t or x^{4} - 4 x^{3} - 21 x^{2}

s im pl i f y 4 lo g_{4} (5) + 5 lo g_{4} (x)