faktorisieren 16m^4+4m^2*n^2+n^4

Lösung

faktorisieren

16 m^{4} + 4 m^{2} \cdot n^{2} + n^{4}

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

Schritte zur Lösung

16 m^{4} + 4 m^{2} n^{2} + n^{4}

Addiere und subtrahiere

4 m^{2} n^{2}

= 16 m^{4} + 8 m^{2} n^{2} + n^{4} - 4 m^{2} n^{2}

Faktorisiere

16 m^{4} + 8 m^{2} n^{2} + n^{4} : (4 m^{2} + n^{2})^{2}

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

Wende Exponentenregel an

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

Faktorisiere

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

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

s im pl i f y \frac{( x ^{2} + 4 x + 4 )}{( 2 + 1 )}

s im pl i f y 5 20 z + 45 z

s im pl i f y 2 ∣ a + b ∣ + 3 ∣ a - b ∣ - ∣ b ∣^{2}

e x p an d (3 x - 5) (2 x + 2)

s im pl i f y (8 x^{- 5})^{- 3}