faktorisieren 25x^2-10x+1-36z^2

Lösung

faktorisieren

25 x^{2} - 10 x + 1 - 36 z^{2}

(5 x - 1 + 6 z) (5 x - 1 - 6 z)

Schritte zur Lösung

25 x^{2} - 10 x + 1 - 36 z^{2}

Faktorisiere

25 x^{2} - 10 x + 1 : (5 x - 1)^{2}

= (5 x - 1)^{2} - 36 z^{2}

Vereinfache

36 z^{2} : (6 z)^{2}

= (5 x - 1)^{2} - (6 z)^{2}

Wende Formel zur Differenz von zwei Quadraten an:

x^{2} - y^{2} = (x + y) (x - y)

(5 x - 1)^{2} - (6 z)^{2} = ((5 x - 1) + 6 z) ((5 x - 1) - 6 z)

= ((5 x - 1) + 6 z) ((5 x - 1) - 6 z)

Apply rule:

(a) = a

(5 x - 1) = 5 x - 1

= (5 x - 1 + 6 z) (5 x - 1 - 6 z)

f a c t or 100 x^{2} - 80 x y + 16 y^{2}

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s im pl i f y \frac{k \cdot ( \frac{27}{2} )}{( \frac{9}{4} ) i}