vereinfachen (sqrt(x)+5x-2)(\sqrt[3]{x}-3sqrt(x))

Lösung

vereinfachen

(x + 5 x - 2) (3 x - 3 x)

6 x^{5} - 3 x + 5 3 x^{4} - 15 x^{3} - 2 3 x + 6 x

Schritte zur Lösung

(x + 5 x - 2) (3 x - 3 x)

Setze Klammern

= x 3 x + x (- 3 x) + 5 x 3 x + 5 x (- 3 x) - 2 3 x - 2 (- 3 x)

Vereinfache

x 3 x + x (- 3 x) + 5 x 3 x + 5 x (- 3 x) - 2 3 x - 2 (- 3 x) : x^{\frac{5}{6}} - 3 x + 5 x^{\frac{4}{3}} - 15 x^{\frac{3}{2}} - 2 3 x + 6 x

= x^{\frac{5}{6}} - 3 x + 5 x^{\frac{4}{3}} - 15 x^{\frac{3}{2}} - 2 3 x + 6 x

x^{\frac{5}{6}} = 6 x^{5}

= 6 x^{5} - 3 x + 5 3 x^{4} - 15 x^{3} - 2 3 x + 6 x

x^{\frac{4}{3}} = 3 x^{4}

= 6 x^{5} - 3 x + 5 3 x^{4} - 15 x^{3} - 2 3 x + 6 x

x^{\frac{3}{2}} = x^{3}

= 6 x^{5} - 3 x + 5 3 x^{4} - 15 x^{3} - 2 3 x + 6 x

e x p an d \frac{( s + 1 ) ( s + 30.1 )}{s}

e x p an d (sec (x) sc x - tan (x)) sec (x)

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

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

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