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Beliebt Algebra >

vereinfachen (2m-n)^3+(2m+n)^3+12m(4m^2-n^2)

Lösung

vereinfachen

(2 m - n)^{3} + (2 m + n)^{3} + 12 m (4 m^{2} - n^{2})

Lösung

64 m^{3}

Schritte zur Lösung

(2 m - n)^{3} + (2 m + n)^{3} + 12 m (4 m^{2} - n^{2})

Schreibe

(2 m - n)^{3}

um:

8 m^{3} - 12 m^{2} n + 6 m n^{2} - n^{3}

= 8 m^{3} - 12 m^{2} n + 6 m n^{2} - n^{3} + (2 m + n)^{3} + 12 m (4 m^{2} - n^{2})

Schreibe

(2 m + n)^{3}

um:

8 m^{3} + 12 m^{2} n + 6 m n^{2} + n^{3}

= 8 m^{3} - 12 m^{2} n + 6 m n^{2} - n^{3} + 8 m^{3} + 12 m^{2} n + 6 m n^{2} + n^{3} + 12 m (4 m^{2} - n^{2})

Schreibe

12 m (4 m^{2} - n^{2})

um:

48 m^{3} - 12 m n^{2}

= 8 m^{3} - 12 m^{2} n + 6 m n^{2} - n^{3} + 8 m^{3} + 12 m^{2} n + 6 m n^{2} + n^{3} + 48 m^{3} - 12 m n^{2}

Fasse gleiche Terme zusammen

= 8 m^{3} + 8 m^{3} + 48 m^{3} - 12 m^{2} n + 12 m^{2} n + 6 m n^{2} + 6 m n^{2} - 12 m n^{2} - n^{3} + n^{3}

Addiere gleiche Elemente:

8 m^{3} + 8 m^{3} + 48 m^{3} = 64 m^{3}

= 64 m^{3} - 12 m^{2} n + 12 m^{2} n + 6 m n^{2} + 6 m n^{2} - 12 m n^{2} - n^{3} + n^{3}

Addiere gleiche Elemente:

- 12 m^{2} n + 12 m^{2} n = 0

= 64 m^{3} + 6 m n^{2} + 6 m n^{2} - 12 m n^{2} - n^{3} + n^{3}

Addiere gleiche Elemente:

6 m n^{2} + 6 m n^{2} - 12 m n^{2} = 0

= 64 m^{3} - n^{3} + n^{3}

Addiere gleiche Elemente:

- n^{3} + n^{3} = 0

= 64 m^{3}

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