erweitern r(2r^2-ar+a^2)^2

Lösung

erweitern

r (2 r^{2} - a r + a^{2})^{2}

4 r^{5} - 4 a r^{4} + 5 a^{2} r^{3} - 2 a^{3} r^{2} + a^{4} r

Schritte zur Lösung

r (2 r^{2} - a r + a^{2})^{2}

(2 r^{2} - a r + a^{2})^{2} = 4 r^{4} - 4 a r^{3} + 5 a^{2} r^{2} - 2 a^{3} r + a^{4}

= r (4 r^{4} - 4 a r^{3} + 5 a^{2} r^{2} - 2 a^{3} r + a^{4})

Setze Klammern

= r \cdot 4 r^{4} + r (- 4 a r^{3}) + r \cdot 5 a^{2} r^{2} + r (- 2 a^{3} r) + r a^{4}

Wende Minus-Plus Regeln an

+ (- a) = - a

= 4 r^{4} r - 4 a r^{3} r + 5 a^{2} r^{2} r - 2 a^{3} rr + a^{4} r

Vereinfache

4 r^{4} r - 4 a r^{3} r + 5 a^{2} r^{2} r - 2 a^{3} rr + a^{4} r : 4 r^{5} - 4 a r^{4} + 5 a^{2} r^{3} - 2 a^{3} r^{2} + a^{4} r

= 4 r^{5} - 4 a r^{4} + 5 a^{2} r^{3} - 2 a^{3} r^{2} + a^{4} r

e x p an d ln x^{2} \frac{x - 2}{x + 3}

e x p an d (8 + 2 x)^{\frac{- 1}{3}}

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

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

e x p an d \frac{5 x ^{6} ( - 6 x tan ( 6 x ) + 7 )}{7 sec ( 6 x )}