vereinfachen 2x(4x-1)(2x+9)(x-sqrt(5))(x+sqrt(5))

Lösung

vereinfachen

2 x (4 x - 1) (2 x + 9) (x - 5) (x + 5)

2 x (4 x - 1) (2 x + 9) (x^{2} - 5)

Schritte zur Lösung

2 x (4 x - 1) (2 x + 9) (x - 5) (x + 5)

Wende Formel zur Differenz von zwei Quadraten an:

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

(x - 5) (x + 5) = x^{2} - (5)^{2}

= 2 x (4 x - 1) (2 x + 9) (x^{2} - (5)^{2})

Vereinfache

x^{2} - (5)^{2} : x^{2} - 5

= 2 x (4 x - 1) (2 x + 9) (x^{2} - 5)

e x p an d (s - 1) (s + 1 + j^{2} π) (s + 1 - j^{2} π)

e x p an d 2 ln^{2} (2) - 2 (2 ln (2) - 2)

e x p an d \frac{10 x ^{3} - 6 x ^{2} + 15}{( x ^{3} - 3 ) ^{2}}

e x p an d (2 n - 3) x + 5 n (x - 4 = 3)

e x p an d (1 + cos (x))^{2} + (- sin (x))