erweitern ((x-a)(x-b)(x-a-d))/((x-c)(x-d)(x-a-b))

Lösung

erweitern

\frac{( x - a ) ( x - b ) ( x - a - d )}{( x - c ) ( x - d ) ( x - a - b )}

\frac{x ^{3} - 2 a x ^{2} - b x ^{2} - d x ^{2} + a ^{2} x + 2 ab x + b d x + a d x - a ^{2} b - ab d}{x ^{3} - a x ^{2} - b x ^{2} - d x ^{2} + a d x + b d x - c x ^{2} + a c x + b c x + d c x - a d c - b d c}

Schritte zur Lösung

\frac{( x - a ) ( x - b ) ( x - a - d )}{( x - c ) ( x - d ) ( x - a - b )}

Multipliziere aus

(x - c) (x - d) (x - a - b) : x^{3} - a x^{2} - b x^{2} - d x^{2} + a d x + b d x - c x^{2} + a c x + b c x + d c x - a d c - b d c

= \frac{( x - a ) ( x - b ) ( x - a - d )}{x ^{3} - a x ^{2} - b x ^{2} - d x ^{2} + a d x + b d x - c x ^{2} + a c x + b c x + d c x - a d c - b d c}

Multipliziere aus

(x - a) (x - b) (x - a - d) : x^{3} - 2 a x^{2} - b x^{2} - d x^{2} + a^{2} x + 2 ab x + b d x + a d x - a^{2} b - ab d

= \frac{x ^{3} - 2 a x ^{2} - b x ^{2} - d x ^{2} + a ^{2} x + 2 ab x + b d x + a d x - a ^{2} b - ab d}{x ^{3} - a x ^{2} - b x ^{2} - d x ^{2} + a d x + b d x - c x ^{2} + a c x + b c x + d c x - a d c - b d c}

e x p an d (2 x) (2 x)

e x p an d - 3 (25 x - 7)^{2} - 49

e x p an d A (- 4, 7) B (6, - 2)

e x p an d e^{x} (- x^{3} + 3 x) - 3

e x p an d (2 sin (x) - 1) (sin (x) - 1)