erweitern ((ax+x)(ay+y))/(a^2)

Lösung

erweitern

\frac{( a x + x ) ( a y + y )}{a ^{2}}

x y + \frac{2 x y}{a} + \frac{x y}{a ^{2}}

Schritte zur Lösung

\frac{( a x + x ) ( a y + y )}{a ^{2}}

Multipliziere aus

(a x + x) (a y + y) : a^{2} x y + 2 a x y + x y

= \frac{a ^{2} x y + 2 a x y + x y}{a ^{2}}

Wende Bruchregel an:

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

\frac{a ^{2} x y + 2 a x y + x y}{a ^{2}} = \frac{a ^{2} x y}{a ^{2}} + \frac{2 a x y}{a ^{2}} + \frac{x y}{a ^{2}}

= \frac{a ^{2} x y}{a ^{2}} + \frac{2 a x y}{a ^{2}} + \frac{x y}{a ^{2}}

Streiche

\frac{a ^{2} x y}{a ^{2}} : x y

= x y + \frac{2 a x y}{a ^{2}} + \frac{x y}{a ^{2}}

Streiche

\frac{2 a x y}{a ^{2}} : \frac{2 x y}{a}

= x y + \frac{2 x y}{a} + \frac{x y}{a ^{2}}

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

e x p an d \frac{1}{s \cdot ( s ^{2} + s + 4 )}

e x p an d (x^{2} + 7 x + 2) (e^{x} - ln (x))

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

e x p an d \frac{x - 9}{x ( x - 3 )}