erweitern (x-1)(x-2)^2(x-3)^3left(x-4)^4

Lösung

erweitern

(x - 1) \cdot (x - 2)^{2} \cdot (x - 3)^{3} l e f t (x - 4)^{4}

e l x^{10} f t - 30 e l x^{9} f t + 400 e l x^{8} f t - 3118 e l x^{7} f t + 15715 e l x^{6} f t - 53428 e l x^{5} f t + 123852 e l x^{4} f t - 192832 e l x^{3} f t + 192384 e l x^{2} f t - 110592 e l x f t + 27648 e l f t

Schritte zur Lösung

(x - 1) (x - 2)^{2} (x - 3)^{3} l e f t (x - 4)^{4}

= e l f t (x - 1) (x - 2)^{2} (x - 3)^{3} (x - 4)^{4}

Wende das Distributivgesetz an:

a (b - c) = ab - a c

a = (x - 2)^{2} (x - 3)^{3} l e f t (x - 4)^{4}, b = x, c = 1

= (x - 2)^{2} (x - 3)^{3} l e f t (x - 4)^{4} x - (x - 2)^{2} (x - 3)^{3} l e f t (x - 4)^{4} \cdot 1

= e l x f t (x - 2)^{2} (x - 3)^{3} (x - 4)^{4} - 1 e l f t (x - 2)^{2} (x - 3)^{3} (x - 4)^{4}

Vereinfache

e l x f t (x - 2)^{2} (x - 3)^{3} (x - 4)^{4} - 1 e l f t (x - 2)^{2} (x - 3)^{3} (x - 4)^{4} : e l x^{10} f t - 30 e l x^{9} f t + 400 e l x^{8} f t - 3118 e l x^{7} f t + 15715 e l x^{6} f t - 53428 e l x^{5} f t + 123852 e l x^{4} f t - 192832 e l x^{3} f t + 192384 e l x^{2} f t - 110592 e l x f t + 27648 e l f t

= e l x^{10} f t - 30 e l x^{9} f t + 400 e l x^{8} f t - 3118 e l x^{7} f t + 15715 e l x^{6} f t - 53428 e l x^{5} f t + 123852 e l x^{4} f t - 192832 e l x^{3} f t + 192384 e l x^{2} f t - 110592 e l x f t + 27648 e l f t

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

e x p an d - \frac{1}{x ( 1 - ln ( x ) )}

e x p an d \frac{192 x ^{2} - 48 x + 5}{( 8 x - 5 ) ^{6}}

e x p an d \frac{- 3 s - 5 - 9 e ^{- 6 s}}{( 2 s + 8 ) ( s + 10 )}

\frac{d}{d y} ((z) (z^{2} - 2 z y + 3 y^{2}))