erweitern (2+3z+z^2)^5

Lösung

erweitern

(2 + 3 z + z^{2})^{5}

z^{10} + 15 z^{9} + 100 z^{8} + 390 z^{7} + 985 z^{6} + 1683 z^{5} + 1970 z^{4} + 1560 z^{3} + 800 z^{2} + 240 z + 32

Schritte zur Lösung

(2 + 3 z + z^{2})^{5}

(2 + 3 z + z^{2})^{5} = (2 + 3 z + z^{2}) (2 + 3 z + z^{2}) (2 + 3 z + z^{2}) (2 + 3 z + z^{2}) (2 + 3 z + z^{2})

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

Multipliziere aus

(2 + 3 z + z^{2}) (2 + 3 z + z^{2}) (2 + 3 z + z^{2}) (2 + 3 z + z^{2}) (2 + 3 z + z^{2}) : z^{10} + 15 z^{9} + 100 z^{8} + 390 z^{7} + 985 z^{6} + 1683 z^{5} + 1970 z^{4} + 1560 z^{3} + 800 z^{2} + 240 z + 32

= z^{10} + 15 z^{9} + 100 z^{8} + 390 z^{7} + 985 z^{6} + 1683 z^{5} + 1970 z^{4} + 1560 z^{3} + 800 z^{2} + 240 z + 32

e x p an d (e^{x} cos (x) - e^{x} sin (x))^{2}

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s im pl i f y (x + 3) (x - 3)