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kgv x^2+2x+1,x^2-6x+9

Lösung

kgv

x^{2} + 2 x + 1, x^{2} - 6 x + 9

(x + 1)^{2} (x - 3)^{2}

Schritte zur Lösung

Finde das kleinste gemeinsame Vielfache von

x^{2} + 2 x + 1, x^{2} - 6 x + 9

Faktorisiere

x^{2} + 2 x + 1 : (x + 1)^{2}

x^{2} + 2 x + 1

Schreibe

x^{2} + 2 x + 1

um:

x^{2} + 2 x \cdot 1 + 1^{2}

x^{2} + 2 x + 1

Schreibe

1

um:

1^{2}

= x^{2} + 2 x + 1^{2}

Schreibe

2 x

um:

2 x \cdot 1

= x^{2} + 2 x \cdot 1 + 1^{2}

= x^{2} + 2 x \cdot 1 + 1^{2}

Wende Formel für perfekte quadratische Gleichungen an:

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

a = x, b = 1

= (x + 1)^{2}

Faktorisiere

x^{2} - 6 x + 9 : (x - 3)^{2}

x^{2} - 6 x + 9

Schreibe

x^{2} - 6 x + 9

um:

x^{2} - 2 x \cdot 3 + 3^{2}

x^{2} - 6 x + 9

Schreibe

9

um:

3^{2}

= x^{2} - 6 x + 3^{2}

Schreibe

6 x

um:

2 x \cdot 3

= x^{2} - 2 x \cdot 3 + 3^{2}

= x^{2} - 2 x \cdot 3 + 3^{2}

Wende Formel für perfekte quadratische Gleichungen an:

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

a = x, b = 3

= (x - 3)^{2}

Multiply each factor with the highest power:

(x + 1)^{2} \cdot (x - 3)^{2}

d ec t o f r a c 0.875

\frac{8}{2} \cdot (2 + 2)

- 2 (4)^{2}

\frac{6}{2} (2 + 1)

l o n g d i v i s i o n \frac{180}{5}