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Beliebt Algebra >

faktorisieren m^{4a+8}-25

Lösung

faktorisieren

m^{4 a + 8} - 25

Lösung

(m^{2 (a + 2)} + 5) (m^{2 (a + 2)} - 5)

Schritte zur Lösung

m^{4 a + 8} - 25

Faktorisiere

4 a + 8 : 4 (a + 2)

= m^{4 (a + 2)} - 25

Wende Exponentenregel an:

a^{b c} = (a^{b})^{c}

m^{4 (a + 2)} = (m^{(a + 2)})^{4}

= (m^{(a + 2)})^{4} - 25

Schreibe

(m^{(a + 2)})^{4} - 25

um:

((m^{(a + 2)})^{2})^{2} - 5^{2}

= ((m^{(a + 2)})^{2})^{2} - 5^{2}

Wende Formel zur Differenz von zwei Quadraten an:

x^{2} - y^{2} = (x + y) (x - y)

((m^{(a + 2)})^{2})^{2} - 5^{2} = ((m^{(a + 2)})^{2} + 5) ((m^{(a + 2)})^{2} - 5)

= ((m^{(a + 2)})^{2} + 5) ((m^{(a + 2)})^{2} - 5)

Vereinfache

((m^{(a + 2)})^{2} + 5) ((m^{(a + 2)})^{2} - 5) : (m^{2 (a + 2)} + 5) (m^{2 (a + 2)} - 5)

= (m^{2 (a + 2)} + 5) (m^{2 (a + 2)} - 5)

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