erweitern sqrt(x^2+2x-1)*(x^2+2x-1)

Lösung

erweitern

x^{2} + 2 x - 1 \cdot (x^{2} + 2 x - 1)

x^{2} x^{2} + 2 x - 1 + 2 x x^{2} + 2 x - 1 - x^{2} + 2 x - 1

Schritte zur Lösung

x^{2} + 2 x - 1 (x^{2} + 2 x - 1)

Wende das Distributivgesetz an:

m (a + b + c) = ma + mb + m c

x^{2} + 2 x - 1 (x^{2} + 2 x - 1) = x^{2} + 2 x - 1 x^{2} + x^{2} + 2 x - 1 \cdot 2 x + x^{2} + 2 x - 1 (- 1)

= x^{2} + 2 x - 1 x^{2} + x^{2} + 2 x - 1 \cdot 2 x + x^{2} + 2 x - 1 (- 1)

Vereinfache

x^{2} + 2 x - 1 x^{2} + x^{2} + 2 x - 1 \cdot 2 x + x^{2} + 2 x - 1 (- 1) : x^{2} x^{2} + 2 x - 1 + 2 x x^{2} + 2 x - 1 - x^{2} + 2 x - 1

= x^{2} x^{2} + 2 x - 1 + 2 x x^{2} + 2 x - 1 - x^{2} + 2 x - 1

s im pl i f y x (1 - x) (f \circ g) x (1 - x)

e x p an d (x y^{2} + x) d x + y x^{2} d y

e x p an d (2 c t + b) t

e x p an d sin^{2} (x) - cos (x) \cdot (sin (x) - cos (x))

e x p an d (e^{5 x}) \cdot (e^{5 x} + 5 x e^{5 x})