erweitern (5x^3(2x-1)^2(5x+2)^3)/((7x-4)^2)

Lösung

erweitern

\frac{5 x ^{3} ( 2 x - 1 ) ^{2} ( 5 x + 2 ) ^{3}}{( 7 x - 4 ) ^{2}}

\frac{2500 x ^{8} + 500 x ^{7} - 1175 x ^{6} - 290 x ^{5} + 140 x ^{4} + 40 x ^{3}}{49 x ^{2} - 56 x + 16}

Schritte zur Lösung

\frac{5 x ^{3} ( 2 x - 1 ) ^{2} ( 5 x + 2 ) ^{3}}{( 7 x - 4 ) ^{2}}

(7 x - 4)^{2} = 49 x^{2} - 56 x + 16

= \frac{5 x ^{3} ( 2 x - 1 ) ^{2} ( 5 x + 2 ) ^{3}}{49 x ^{2} - 56 x + 16}

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

= \frac{5 x ^{3} ( 4 x ^{2} - 4 x + 1 ) ( 5 x + 2 ) ^{3}}{49 x ^{2} - 56 x + 16}

(5 x + 2)^{3} = 125 x^{3} + 150 x^{2} + 60 x + 8

= \frac{5 x ^{3} ( 4 x ^{2} - 4 x + 1 ) ( 125 x ^{3} + 150 x ^{2} + 60 x + 8 )}{49 x ^{2} - 56 x + 16}

Multipliziere aus

5 x^{3} (4 x^{2} - 4 x + 1) (125 x^{3} + 150 x^{2} + 60 x + 8) : 2500 x^{8} + 500 x^{7} - 1175 x^{6} - 290 x^{5} + 140 x^{4} + 40 x^{3}

= \frac{2500 x ^{8} + 500 x ^{7} - 1175 x ^{6} - 290 x ^{5} + 140 x ^{4} + 40 x ^{3}}{49 x ^{2} - 56 x + 16}

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

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

e x p an d 3 x^{2} + 3 (x - 1)^{2}

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

s im pl i f y 9 (sin^{4} (+ cos^{4} (u))) - 6 (sin^{6} (u) + cos^{6} (u))