faktorisieren 100m^2n^3-50m^3n^4+150m^2n^2

Lösung

faktorisieren

100 m^{2} n^{3} - 50 m^{3} n^{4} + 150 m^{2} n^{2}

50 m^{2} n^{2} (2 n - m n^{2} + 3)

Schritte zur Lösung

100 m^{2} n^{3} - 50 m^{3} n^{4} + 150 m^{2} n^{2}

Wende Exponentenregel an:

a^{b + c} = a^{b} a^{c}

m^{2} n^{3} = m^{2} n^{2} n, m^{3} n^{4} = m^{2} m n^{2} n^{2}

= 100 m^{2} n^{2} n - 50 m^{2} m n^{2} n^{2} + 150 m^{2} n^{2}

Schreibe

150

um:

3 \cdot 50

Schreibe

100

um:

2 \cdot 50

= 2 \cdot 50 m^{2} n^{2} n - 50 m^{2} m n^{2} n^{2} + 3 \cdot 50 m^{2} n^{2}

Klammere gleiche Terme aus

50 m^{2} n^{2}

= 50 m^{2} n^{2} (2 n - m n^{2} + 3)

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s im pl i f y (lo g_{10} (a) lo g_{10} (c) b lo g_{10} (a))^{3}

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