faktorisieren ((x+h)^3-x^3)/h

Lösung

faktorisieren

\frac{( x + h ) ^{3} - x ^{3}}{h}

3 x^{2} + 3 x h + h^{2}

Schritte zur Lösung

\frac{( x + h ) ^{3} - x ^{3}}{h}

Faktorisiere

(x + h)^{3} - x^{3} : h ((x + h)^{2} + x (x + h) + x^{2})

= \frac{h ( ( x + h ) ^{2} + x ( x + h ) + x ^{2} )}{h}

Streiche die gemeinsamen Faktoren:

h

= (x + h)^{2} + x (x + h) + x^{2}

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

= x^{2} + 2 x h + h^{2} + x (x + h) + x^{2}

Multipliziere aus

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

= x^{2} + 2 x h + h^{2} + x^{2} + x h + x^{2}

Vereinfache

x^{2} + 2 x h + h^{2} + x^{2} + x h + x^{2} : 3 x^{2} + 3 x h + h^{2}

= 3 x^{2} + 3 x h + h^{2}

- 3 x + 24 < 22.5

∣ x + 5 ∣ < - 5

f a c t or 2 x^{2} - 4 x + x y - 2 y

25 x (10 x^{12}) = (25 x^{10}) x^{12}

s im pl i f y \frac{\frac{26}{5}}{( - 5 )}