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

Lösung

erweitern

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

\frac{8 x ^{3} + 36 x ^{2} + 54 x + 27}{65536 x ^{16} - 131072 x ^{14} + 114688 x ^{12} - 57344 x ^{10} + 17920 x ^{8} - 3584 x ^{6} + 448 x ^{4} - 32 x ^{2} + 1}

Schritte zur Lösung

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

(4 x^{2} - 1)^{8} = 65536 x^{16} - 131072 x^{14} + 114688 x^{12} - 57344 x^{10} + 17920 x^{8} - 3584 x^{6} + 448 x^{4} - 32 x^{2} + 1

= \frac{( 2 x + 3 ) ^{3}}{65536 x ^{16} - 131072 x ^{14} + 114688 x ^{12} - 57344 x ^{10} + 17920 x ^{8} - 3584 x ^{6} + 448 x ^{4} - 32 x ^{2} + 1}

(2 x + 3)^{3} = 8 x^{3} + 36 x^{2} + 54 x + 27

= \frac{8 x ^{3} + 36 x ^{2} + 54 x + 27}{65536 x ^{16} - 131072 x ^{14} + 114688 x ^{12} - 57344 x ^{10} + 17920 x ^{8} - 3584 x ^{6} + 448 x ^{4} - 32 x ^{2} + 1}

e x p an d \frac{100}{( s + 2 ) ( s + 3 ) ( s + 5 )}

e x p an d (y - (- 4)) \cdot y^{2} (y = - 1)

e x p an d sin (2 θ + θ)

e x p an d \frac{6 x ^{2} + 4 x}{( x + 2 ) ^{2} ( x - 1 )}

e x p an d \frac{6 x ^{2} - 11 x - 32}{( x + 6 ) ( x + 1 ) ^{2}}