vereinfachen x(ax-1)(ax-a-1)(x+1)+a

Lösung

vereinfachen

x (a x - 1) (a x - a - 1) (x + 1) + a

x^{4} a^{2} - 2 a x^{3} - x^{2} a^{2} + x^{2} - a x^{2} + a x + x + a

Schritte zur Lösung

x (a x - 1) (a x - a - 1) (x + 1) + a

Apply FOIL method

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

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

Schreibe

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

um:

a^{2} x^{3} - 2 a x^{2} - x a^{2} + x - a x + a + 1

= x (a^{2} x^{3} - 2 a x^{2} - x a^{2} + x - a x + a + 1) + a

Setze Klammern

= x a^{2} x^{3} + x (- 2 a x^{2}) + x (- x a^{2}) + xx + x (- a x) + x a + x \cdot 1 + a

Vereinfache

x a^{2} x^{3} + x (- 2 a x^{2}) + x (- x a^{2}) + xx + x (- a x) + x a + x \cdot 1 : x^{4} a^{2} - 2 a x^{3} - x^{2} a^{2} + x^{2} - a x^{2} + a x + x

= x^{4} a^{2} - 2 a x^{3} - x^{2} a^{2} + x^{2} - a x^{2} + a x + x + a

s im pl i f y 2 ab + 3 ab + ab

s im pl i f y x^{2} x^{3}

s im pl i f y (9 x^{2} + 4 x) - (- 4 x^{2} - 7)

e x p an d (x + 1) (1 - x)

s im pl i f y (- 5 x^{- 3})^{2}