erweitern (((q-p))/2)^2+q*p

Lösung

erweitern

(\frac{( q - p )}{2})^{2} + q \cdot p

\frac{q ^{2}}{4} + \frac{qp}{2} + \frac{p ^{2}}{4}

Schritte zur Lösung

(\frac{q - p}{2})^{2} + qp

(\frac{q - p}{2})^{2} = \frac{q ^{2} - 2 qp + p ^{2}}{2 ^{2}}

= \frac{q ^{2} - 2 qp + p ^{2}}{2 ^{2}} + qp

Wandle das Element in einen Bruch um:

qp = \frac{qp 2 ^{2}}{2 ^{2}}

= \frac{q ^{2} - 2 qp + p ^{2}}{2 ^{2}} + \frac{qp \cdot 2 ^{2}}{2 ^{2}}

Da die Nenner gleich sind, fasse die Brüche zusammen.:

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

= \frac{q ^{2} - 2 qp + p ^{2} + qp \cdot 2 ^{2}}{2 ^{2}}

q^{2} - 2 qp + p^{2} + qp \cdot 2^{2} = q^{2} + 2 qp + p^{2}

= \frac{q ^{2} + 2 qp + p ^{2}}{2 ^{2}}

2^{2} = 4

= \frac{q ^{2} + 2 qp + p ^{2}}{4}

Wende Bruchregel an:

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

\frac{q ^{2} + 2 qp + p ^{2}}{4} = \frac{q ^{2}}{4} + \frac{2 qp}{4} + \frac{p ^{2}}{4}

= \frac{q ^{2}}{4} + \frac{2 qp}{4} + \frac{p ^{2}}{4}

Streiche

\frac{2 qp}{4} : \frac{qp}{2}

= \frac{q ^{2}}{4} + \frac{qp}{2} + \frac{p ^{2}}{4}

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

e x p an d (1 + x^{4}) d y + x (1 + 4 y^{2})

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

e x p an d (- b sin (t) + b cos (t) + 1 - b)^{3}

e x p an d e^{x} (c_{1} cos (2 x) + c_{2} sin (2 x))