faktorisieren 9/25 a^2-49/36 b^2

Lösung

faktorisieren

\frac{9}{25} a^{2} - \frac{49}{36} b^{2}

(\frac{3}{5} a + \frac{7}{6} b) (\frac{3}{5} a - \frac{7}{6} b)

Schritte zur Lösung

\frac{9}{25} a^{2} - \frac{49}{36} b^{2}

\frac{9}{25} a^{2} = (\frac{3}{5} a)^{2}

\frac{49}{36} b^{2} = (\frac{7}{6} b)^{2}

= (\frac{3}{5} a)^{2} - (\frac{7}{6} b)^{2}

Wende Formel zur Differenz von zwei Quadraten an:

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

(\frac{3}{5} a)^{2} - (\frac{7}{6} b)^{2} = (\frac{3}{5} a + \frac{7}{6} b) (\frac{3}{5} a - \frac{7}{6} b)

= (\frac{3}{5} a + \frac{7}{6} b) (\frac{3}{5} a - \frac{7}{6} b)

e x p an d (x - a) (x + a)

s im pl i f y \frac{15 - \frac{2}{x}}{\frac{x}{5} + 4}

s im pl i f y 2 \times \frac{4}{3}

e x p an d (5 x^{3} - 4 x^{2} + x) (- 3 x^{2} + 6 x - 7)

s im pl i f y \frac{2}{18}