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 C (- 1, - 7) P (2, - 3)

e x p an d (a^{2} + 3 a + 2)^{9}

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

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

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