faktorisieren a^2+2a(a+b)+(a+b)^2

Lösung

faktorisieren

a^{2} + 2 a (a + b) + (a + b)^{2}

(2 a + b)^{2}

Schritte zur Lösung

a^{2} + 2 a (a + b) + (a + b)^{2}

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

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

Multipliziere aus

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

= a^{2} + 2 a^{2} + 2 ab + a^{2} + 2 ab + b^{2}

Vereinfache

a^{2} + 2 a^{2} + 2 ab + a^{2} + 2 ab + b^{2} : 4 a^{2} + 4 ab + b^{2}

= 4 a^{2} + 4 ab + b^{2}

Schreibe

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

um:

(2 a)^{2} + 2 \cdot 2 ab + b^{2}

= (2 a)^{2} + 2 \cdot 2 ab + b^{2}

Wende Formel für perfekte quadratische Gleichungen an:

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

a = 2 a, b = b

= (2 a + b)^{2}

f a c t or 10 + 221

f a c t or (5 p^{2} - 3) + (2 p - 3 p^{3})

f a c t or (x + Δ)^{(2)} - 4 (x + Δ)

f a c t or 17 d^{9} e^{4} - 51 e^{6}

f a c t or [(m - 3) + n] [(m - 3) - n]