faktorisieren 9m^4+14m^2n^2+25n^4

Lösung

faktorisieren

9 m^{4} + 14 m^{2} n^{2} + 25 n^{4}

(3 m^{2} + 5 n^{2} + 4 mn) (3 m^{2} + 5 n^{2} - 4 mn)

Schritte zur Lösung

9 m^{4} + 14 m^{2} n^{2} + 25 n^{4}

Addiere und subtrahiere

16 m^{2} n^{2}

= 9 m^{4} + 30 m^{2} n^{2} + 25 n^{4} - 16 m^{2} n^{2}

Faktorisiere

9 m^{4} + 30 m^{2} n^{2} + 25 n^{4} : (3 m^{2} + 5 n^{2})^{2}

= (3 m^{2} + 5 n^{2})^{2} - 16 m^{2} n^{2}

Wende Exponentenregel an

= (3 m^{2} + 5 n^{2})^{2} - (4 mn)^{2}

Faktorisiere

(3 m^{2} + 5 n^{2})^{2} - (4 mn)^{2} : (3 m^{2} + 5 n^{2} + 4 mn) (3 m^{2} + 5 n^{2} - 4 mn)

= (3 m^{2} + 5 n^{2} + 4 mn) (3 m^{2} + 5 n^{2} - 4 mn)

s im pl i f y \frac{6 y ^{5} + 4 y ^{3} - 10 y ^{2} + 2 y}{2 y}

s im pl i f y sin^{2} (q) + cos^{2} (q)

s im pl i f y \frac{( 2 - x )}{( x - 2 )}

s im pl i f y \frac{( 4 x ^{2} + 10 x )}{( 2 x )}

s im pl i f y 400 (m^{1})^{0} n^{4} - 280 m^{5} n^{2} y^{3} + 49 y^{6}