faktorisieren 121r^3s^4+77r^2s^4-55r^4s^3

Lösung

faktorisieren

121 r^{3} s^{4} + 77 r^{2} s^{4} - 55 r^{4} s^{3}

11 r^{2} s^{3} (11 rs + 7 s - 5 r^{2})

Schritte zur Lösung

121 r^{3} s^{4} + 77 r^{2} s^{4} - 55 r^{4} s^{3}

Wende Exponentenregel an:

a^{b + c} = a^{b} a^{c}

r^{3} s^{4} = r^{2} r s^{3} s, r^{2} s^{4} = r^{2} s^{3} s, r^{4} s^{3} = r^{2} r^{2} s^{3}

= 121 r^{2} r s^{3} s + 77 r^{2} s^{3} s - 55 r^{2} r^{2} s^{3}

Schreibe

- 55

um:

5 \cdot 11

Schreibe

77

um:

7 \cdot 11

= 11 \cdot 11 r^{2} r s^{3} s + 7 \cdot 11 r^{2} s^{3} s + 5 \cdot 11 r^{2} r^{2} s^{3}

Klammere gleiche Terme aus

11 r^{2} s^{3}

= 11 r^{2} s^{3} (11 rs + 7 s - 5 r^{2})

s im pl i f y (37)^{2}

x^{2} - 2 x + 1 = 16 (x - 4)

f a c t or x y^{3} - 9 x y z^{2}

3 (x - 3) = 6

f a c t or x^{3} - 3 x^{2} - 2 x + 6