faktorisieren 9a^4-a^2-12a-36

Lösung

faktorisieren

9 a^{4} - a^{2} - 12 a - 36

(3 a^{2} + a + 6) (3 a^{2} - a - 6)

Schritte zur Lösung

9 a^{4} - a^{2} - 12 a - 36

Faktorisiere

- a^{2} - 12 a - 36 : - (a + 6)^{2}

= 9 a^{4} - (a + 6)^{2}

Vereinfache

9 a^{4} : (3 a^{2})^{2}

= (3 a^{2})^{2} - (a + 6)^{2}

Wende Formel zur Differenz von zwei Quadraten an:

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

(3 a^{2})^{2} - (a + 6)^{2} = (3 a^{2} + (a + 6)) (3 a^{2} - (a + 6))

= (3 a^{2} + (a + 6)) (3 a^{2} - (a + 6))

Vereinfache

(3 a^{2} + (a + 6)) (3 a^{2} - (a + 6)) : (3 a^{2} + a + 6) (3 a^{2} - a - 6)

= (3 a^{2} + a + 6) (3 a^{2} - a - 6)

s im pl i f y (2 x + 5)^{3} - (2 x - 5)^{3}

s im pl i f y (\frac{f}{g}) (1)

f a c t or 25 x^{12} + 25 x^{6} \cdot y + 25 y^{2}

s im pl i f y \frac{( 3 y ^{2} + 8 y + 4 )}{( y ^{2} - 4 )}

s im pl i f y (- 2^{- 1} x^{- n})^{- 3}