faktorisieren m^7+a^7x^7

Lösung

faktorisieren

m^{7} + a^{7} x^{7}

(m + a x) (m^{6} - m^{5} a x + m^{4} a^{2} x^{2} - m^{3} a^{3} x^{3} + m^{2} a^{4} x^{4} - m a^{5} x^{5} + a^{6} x^{6})

Schritte zur Lösung

m^{7} + a^{7} x^{7}

Schreibe

a^{7} x^{7}

um:

(a x)^{7}

= m^{7} + (a x)^{7}

Wende Regel zum Faktorisieren an:

x^{n} + y^{n} = (x + y) (x^{n - 1} - x^{n - 2} y + \dots - x y^{n - 2} + y^{n - 1})

n is odd

m^{7} + (a x)^{7} = (m + a x) (m^{6} - m^{5} a x + m^{4} (a x)^{2} - m^{3} (a x)^{3} + m^{2} (a x)^{4} - m (a x)^{5} + (a x)^{6})

= (m + a x) (m^{6} - m^{5} a x + m^{4} (a x)^{2} - m^{3} (a x)^{3} + m^{2} (a x)^{4} - m (a x)^{5} + (a x)^{6})

Vereinfache

(m + a x) (m^{6} - m^{5} a x + m^{4} (a x)^{2} - m^{3} (a x)^{3} + m^{2} (a x)^{4} - m (a x)^{5} + (a x)^{6}) : (m + a x) (m^{6} - m^{5} a x + m^{4} a^{2} x^{2} - m^{3} a^{3} x^{3} + m^{2} a^{4} x^{4} - m a^{5} x^{5} + a^{6} x^{6})

= (m + a x) (m^{6} - m^{5} a x + m^{4} a^{2} x^{2} - m^{3} a^{3} x^{3} + m^{2} a^{4} x^{4} - m a^{5} x^{5} + a^{6} x^{6})

f a c t or (x + 3)^{3} - 8

f a c t or A u (N O^{3}) 3

f a c t or 0.064 x^{27} - 1.331 b^{15}

\frac{d}{d t} ((x) (t cos (t)))

f a c t or 3 a^{2} - 9 ab - 5 a c + 15 b c