faktorisieren 16a^4+4a^2b^2+b^4

Lösung

faktorisieren

16 a^{4} + 4 a^{2} b^{2} + b^{4}

(4 a^{2} + b^{2} + 2 ab) (4 a^{2} + b^{2} - 2 ab)

Schritte zur Lösung

16 a^{4} + 4 a^{2} b^{2} + b^{4}

Addiere und subtrahiere

4 a^{2} b^{2}

= 16 a^{4} + 8 a^{2} b^{2} + b^{4} - 4 a^{2} b^{2}

Faktorisiere

16 a^{4} + 8 a^{2} b^{2} + b^{4} : (4 a^{2} + b^{2})^{2}

= (4 a^{2} + b^{2})^{2} - 4 a^{2} b^{2}

Wende Exponentenregel an

= (4 a^{2} + b^{2})^{2} - (2 ab)^{2}

Faktorisiere

(4 a^{2} + b^{2})^{2} - (2 ab)^{2} : (4 a^{2} + b^{2} + 2 ab) (4 a^{2} + b^{2} - 2 ab)

= (4 a^{2} + b^{2} + 2 ab) (4 a^{2} + b^{2} - 2 ab)

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

f a c t or a^{3} b^{3} + 8

s im pl i f y - 3 (2 x + 1) + 3 (4 - x)

f a c t or 3 x^{8} - x^{2}

f a c t or 4 x^{2} - 49 n^{2}