erweitern x^3(5x^2-x+1)^2

Lösung

erweitern

x^{3} (5 x^{2} - x + 1)^{2}

25 x^{7} - 10 x^{6} + 11 x^{5} - 2 x^{4} + x^{3}

Schritte zur Lösung

x^{3} (5 x^{2} - x + 1)^{2}

(5 x^{2} - x + 1)^{2} = 25 x^{4} - 10 x^{3} + 11 x^{2} - 2 x + 1

= x^{3} (25 x^{4} - 10 x^{3} + 11 x^{2} - 2 x + 1)

Setze Klammern

= x^{3} \cdot 25 x^{4} + x^{3} (- 10 x^{3}) + x^{3} \cdot 11 x^{2} + x^{3} (- 2 x) + x^{3} \cdot 1

Wende Minus-Plus Regeln an

+ (- a) = - a

= 25 x^{4} x^{3} - 10 x^{3} x^{3} + 11 x^{3} x^{2} - 2 x^{3} x + 1 \cdot x^{3}

Vereinfache

25 x^{4} x^{3} - 10 x^{3} x^{3} + 11 x^{3} x^{2} - 2 x^{3} x + 1 \cdot x^{3} : 25 x^{7} - 10 x^{6} + 11 x^{5} - 2 x^{4} + x^{3}

= 25 x^{7} - 10 x^{6} + 11 x^{5} - 2 x^{4} + x^{3}

e x p an d \frac{( y - 6 ) ( y + 3 )}{( 2 y + 3 )}

e x p an d 2 cos (2) (θ - \frac{π}{4}) + 1

e x p an d e^{x} \cdot (e^{x} + x e^{x})

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

e x p an d - \frac{13}{( 2 x - 3 ) ^{2}}