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Beliebt Algebra >

erweitern (5x^3+3x^2)*10(-4x+5)^9

Lösung

erweitern

(5 x^{3} + 3 x^{2}) \cdot 10 (- 4 x + 5)^{9}

Lösung

- 13107200 x^{12} + 139591680 x^{11} - 648806400 x^{10} + 1708032000 x^{9} - 2741760000 x^{8} + 2620800000 x^{7} - 1176000000 x^{6} - 270000000 x^{5} + 646875000 x^{4} - 324218750 x^{3} + 58593750 x^{2}

Schritte zur Lösung

(5 x^{3} + 3 x^{2}) \cdot 10 (- 4 x + 5)^{9}

= 10 (- 4 x + 5)^{9} (5 x^{3} + 3 x^{2})

Wende das Distributivgesetz an:

a (b + c) = ab + a c

10 (- 4 x + 5)^{9} (5 x^{3} + 3 x^{2}) = 10 (- 4 x + 5)^{9} \cdot 5 x^{3} + 10 (- 4 x + 5)^{9} \cdot 3 x^{2}

= 10 (- 4 x + 5)^{9} \cdot 5 x^{3} + 10 (- 4 x + 5)^{9} \cdot 3 x^{2}

Vereinfache

10 (- 4 x + 5)^{9} \cdot 5 x^{3} + 10 (- 4 x + 5)^{9} \cdot 3 x^{2} : 50 x^{3} (- 4 x + 5)^{9} + 30 x^{2} (- 4 x + 5)^{9}

= 50 x^{3} (- 4 x + 5)^{9} + 30 x^{2} (- 4 x + 5)^{9}

Schreibe

50 x^{3} (- 4 x + 5)^{9}

um:

- 13107200 x^{12} + 147456000 x^{11} - 737280000 x^{10} + 2150400000 x^{9} - 4032000000 x^{8} + 5040000000 x^{7} - 4200000000 x^{6} + 2250000000 x^{5} - 703125000 x^{4} + 97656250 x^{3}

= - 13107200 x^{12} + 147456000 x^{11} - 737280000 x^{10} + 2150400000 x^{9} - 4032000000 x^{8} + 5040000000 x^{7} - 4200000000 x^{6} + 2250000000 x^{5} - 703125000 x^{4} + 97656250 x^{3} + 30 x^{2} (- 4 x + 5)^{9}

Schreibe

30 x^{2} (- 4 x + 5)^{9}

um:

- 7864320 x^{11} + 88473600 x^{10} - 442368000 x^{9} + 1290240000 x^{8} - 2419200000 x^{7} + 3024000000 x^{6} - 2520000000 x^{5} + 1350000000 x^{4} - 421875000 x^{3} + 58593750 x^{2}

= - 13107200 x^{12} + 147456000 x^{11} - 737280000 x^{10} + 2150400000 x^{9} - 4032000000 x^{8} + 5040000000 x^{7} - 4200000000 x^{6} + 2250000000 x^{5} - 703125000 x^{4} + 97656250 x^{3} - 7864320 x^{11} + 88473600 x^{10} - 442368000 x^{9} + 1290240000 x^{8} - 2419200000 x^{7} + 3024000000 x^{6} - 2520000000 x^{5} + 1350000000 x^{4} - 421875000 x^{3} + 58593750 x^{2}

Vereinfache

- 13107200 x^{12} + 147456000 x^{11} - 737280000 x^{10} + 2150400000 x^{9} - 4032000000 x^{8} + 5040000000 x^{7} - 4200000000 x^{6} + 2250000000 x^{5} - 703125000 x^{4} + 97656250 x^{3} - 7864320 x^{11} + 88473600 x^{10} - 442368000 x^{9} + 1290240000 x^{8} - 2419200000 x^{7} + 3024000000 x^{6} - 2520000000 x^{5} + 1350000000 x^{4} - 421875000 x^{3} + 58593750 x^{2} : - 13107200 x^{12} + 139591680 x^{11} - 648806400 x^{10} + 1708032000 x^{9} - 2741760000 x^{8} + 2620800000 x^{7} - 1176000000 x^{6} - 270000000 x^{5} + 646875000 x^{4} - 324218750 x^{3} + 58593750 x^{2}

= - 13107200 x^{12} + 139591680 x^{11} - 648806400 x^{10} + 1708032000 x^{9} - 2741760000 x^{8} + 2620800000 x^{7} - 1176000000 x^{6} - 270000000 x^{5} + 646875000 x^{4} - 324218750 x^{3} + 58593750 x^{2}

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