erweitern (5(x+h)^2+4(x+h))/h

Lösung

erweitern

\frac{5 ( x + h ) ^{2} + 4 ( x + h )}{h}

\frac{5 x ^{2}}{h} + 10 x + 5 h + \frac{4 x}{h} + 4

Schritte zur Lösung

\frac{5 ( x + h ) ^{2} + 4 ( x + h )}{h}

(x + h)^{2} = x^{2} + 2 x h + h^{2}

= \frac{5 ( x ^{2} + 2 x h + h ^{2} ) + 4 ( x + h )}{h}

Multipliziere aus

5 (x^{2} + 2 x h + h^{2}) + 4 (x + h) : 5 x^{2} + 10 x h + 5 h^{2} + 4 x + 4 h

= \frac{5 x ^{2} + 10 x h + 5 h ^{2} + 4 x + 4 h}{h}

Wende Bruchregel an:

\frac{a \pm b}{c} = \frac{a}{c} \pm \frac{b}{c}

\frac{5 x ^{2} + 10 x h + 5 h ^{2} + 4 x + 4 h}{h} = \frac{5 x ^{2}}{h} + \frac{10 x h}{h} + \frac{5 h ^{2}}{h} + \frac{4 x}{h} + \frac{4 h}{h}

= \frac{5 x ^{2}}{h} + \frac{10 x h}{h} + \frac{5 h ^{2}}{h} + \frac{4 x}{h} + \frac{4 h}{h}

Streiche

\frac{10 x h}{h} : 10 x

= \frac{5 x ^{2}}{h} + 10 x + \frac{5 h ^{2}}{h} + \frac{4 x}{h} + \frac{4 h}{h}

Streiche

\frac{5 h ^{2}}{h} : 5 h

= \frac{5 x ^{2}}{h} + 10 x + 5 h + \frac{4 x}{h} + \frac{4 h}{h}

Streiche

\frac{4 h}{h} : 4

= \frac{5 x ^{2}}{h} + 10 x + 5 h + \frac{4 x}{h} + 4

e x p an d \frac{9 ( 1 - n ^{3} )}{5}

e x p an d π (\frac{3}{3} + 1)

s im pl i f y (O e + O i) (D i + De)

e x p an d (ln (6) - 1)^{2}

e x p an d 5 a^{2} b^{4} \cdot 2