erweitern ((x-1)^4n(x^3+8)(x-4))/((x^2-2x+2))

Lösung

erweitern

\frac{( x - 1 ) ^{4} n ( x ^{3} + 8 ) ( x - 4 )}{( x ^{2} - 2 x + 2 )}

\frac{n x ^{8} - 8 n x ^{7} + 22 n x ^{6} - 20 n x ^{5} - 47 n x ^{4} + 172 n x ^{3} - 224 n x ^{2} + 136 n x - 32 n}{x ^{2} - 2 x + 2}

Schritte zur Lösung

\frac{( x - 1 ) ^{4} n ( x ^{3} + 8 ) ( x - 4 )}{x ^{2} - 2 x + 2}

(x - 1)^{4} = x^{4} - 4 x^{3} + 6 x^{2} - 4 x + 1

= \frac{n ( x ^{4} - 4 x ^{3} + 6 x ^{2} - 4 x + 1 ) ( x ^{3} + 8 ) ( x - 4 )}{x ^{2} - 2 x + 2}

Multipliziere aus

(x^{4} - 4 x^{3} + 6 x^{2} - 4 x + 1) n (x^{3} + 8) (x - 4) : n x^{8} - 8 n x^{7} + 22 n x^{6} - 20 n x^{5} - 47 n x^{4} + 172 n x^{3} - 224 n x^{2} + 136 n x - 32 n

= \frac{n x ^{8} - 8 n x ^{7} + 22 n x ^{6} - 20 n x ^{5} - 47 n x ^{4} + 172 n x ^{3} - 224 n x ^{2} + 136 n x - 32 n}{x ^{2} - 2 x + 2}

e x p an d (3 + 4 y^{2} + 4 y)^{5}

e x p an d \frac{x - 2}{x ( x - 1 )}

e x p an d \frac{1}{( 0.002 s ^{2} + 0.02 s + 1 ) ( s ^{2} + 0.1 s + 1 )}

e x p an d \frac{4 ( 4 x + 1 )}{x}

e x p an d 3 (x + d x)^{2}