erweitern (1+X^4+X^6)^7

Lösung

erweitern

(1 + X^{4} + X^{6})^{7}

X^{42} + 7 X^{40} + 21 X^{38} + 42 X^{36} + 77 X^{34} + 126 X^{32} + 168 X^{30} + 211 X^{28} + 252 X^{26} + 252 X^{24} + 245 X^{22} + 231 X^{20} + 175 X^{18} + 140 X^{16} + 105 X^{14} + 56 X^{12} + 42 X^{10} + 21 X^{8} + 7 X^{6} + 7 X^{4} + 1

Schritte zur Lösung

(1 + X^{4} + X^{6})^{7}

(1 + X^{4} + X^{6})^{7} = (1 + X^{4} + X^{6}) (1 + X^{4} + X^{6}) (1 + X^{4} + X^{6}) (1 + X^{4} + X^{6}) (1 + X^{4} + X^{6}) (1 + X^{4} + X^{6}) (1 + X^{4} + X^{6})

= (X^{6} + X^{4} + 1) (X^{6} + X^{4} + 1) (X^{6} + X^{4} + 1) (X^{6} + X^{4} + 1) (X^{6} + X^{4} + 1) (X^{6} + X^{4} + 1) (X^{6} + X^{4} + 1)

Multipliziere aus

(1 + X^{4} + X^{6}) (1 + X^{4} + X^{6}) (1 + X^{4} + X^{6}) (1 + X^{4} + X^{6}) (1 + X^{4} + X^{6}) (1 + X^{4} + X^{6}) (1 + X^{4} + X^{6}) : X^{42} + 7 X^{40} + 21 X^{38} + 42 X^{36} + 77 X^{34} + 126 X^{32} + 168 X^{30} + 211 X^{28} + 252 X^{26} + 252 X^{24} + 245 X^{22} + 231 X^{20} + 175 X^{18} + 140 X^{16} + 105 X^{14} + 56 X^{12} + 42 X^{10} + 21 X^{8} + 7 X^{6} + 7 X^{4} + 1

= X^{42} + 7 X^{40} + 21 X^{38} + 42 X^{36} + 77 X^{34} + 126 X^{32} + 168 X^{30} + 211 X^{28} + 252 X^{26} + 252 X^{24} + 245 X^{22} + 231 X^{20} + 175 X^{18} + 140 X^{16} + 105 X^{14} + 56 X^{12} + 42 X^{10} + 21 X^{8} + 7 X^{6} + 7 X^{4} + 1

e x p an d (x + π x)^{3}

e x p an d (x^{3} + x y^{2} + a^{2} y) d x

e x p an d \frac{x + 77}{x ( x + 11 )}

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

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