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

Lösung

erweitern

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

\frac{16 x ^{4} - 48 x ^{3} + 4 x ^{2} + 48 x + 16}{1 - 10 x + 36 x ^{2} - 54 x ^{3} + 27 x ^{4}}

Schritte zur Lösung

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

(1 - 3 x)^{3} = 1 - 9 x + 27 x^{2} - 27 x^{3}

= \frac{( - 2 x + 4 ) ^{2} ( 2 x + 1 ) ^{2}}{( - 27 x ^{3} + 27 x ^{2} - 9 x + 1 ) ( - x + 1 )}

(4 - 2 x)^{2} = 16 - 16 x + 4 x^{2}

= \frac{( 4 x ^{2} - 16 x + 16 ) ( 2 x + 1 ) ^{2}}{( - 27 x ^{3} + 27 x ^{2} - 9 x + 1 ) ( - x + 1 )}

(1 + 2 x)^{2} = 1 + 4 x + 4 x^{2}

= \frac{( 4 x ^{2} - 16 x + 16 ) ( 4 x ^{2} + 4 x + 1 )}{( - 27 x ^{3} + 27 x ^{2} - 9 x + 1 ) ( - x + 1 )}

Multipliziere aus

(1 - 9 x + 27 x^{2} - 27 x^{3}) (1 - x) : 1 - 10 x + 36 x^{2} - 54 x^{3} + 27 x^{4}

= \frac{( 4 x ^{2} - 16 x + 16 ) ( 4 x ^{2} + 4 x + 1 )}{1 - 10 x + 36 x ^{2} - 54 x ^{3} + 27 x ^{4}}

Multipliziere aus

(16 - 16 x + 4 x^{2}) (1 + 4 x + 4 x^{2}) : 16 x^{4} - 48 x^{3} + 4 x^{2} + 48 x + 16

= \frac{16 x ^{4} - 48 x ^{3} + 4 x ^{2} + 48 x + 16}{1 - 10 x + 36 x ^{2} - 54 x ^{3} + 27 x ^{4}}

e x p an d (1 + \frac{2 x}{y})^{3}

e x p an d 3 (t + Δ t)^{2} (- sin (Δ t) + cos (Δ t))

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

e x p an d \frac{( ( n + 1 ) ^{2} ( 2 n ^{2} + 2 n - 1 ) )}{n ^{4}}

e x p an d \frac{6 ( P - u w )}{L ( 4 P - 3 u w )}