faktorisieren 9/4 p^2+3/2 pq+1/4 q^2

Lösung

faktorisieren

\frac{9}{4} p^{2} + \frac{3}{2} pq + \frac{1}{4} q^{2}

(\frac{3 p}{2} + \frac{q}{2})^{2}

Schritte zur Lösung

\frac{9}{4} p^{2} + \frac{3}{2} pq + \frac{1}{4} q^{2}

Rewrite in the form of

a^{2} + 2 ab + b^{2} :

\frac{9 p ^{2}}{4} = (\frac{3}{2} p)^{2}

\frac{q ^{2}}{4} = (\frac{1}{2} q)^{2}

\frac{3 pq}{2} = 2 \cdot \frac{3}{2} p \frac{1}{2} q

= (\frac{3}{2} p)^{2} + 2 \cdot \frac{3}{2} p \frac{1}{2} q + (\frac{1}{2} q)^{2}

Wende Formel für perfekte quadratische Gleichungen an:

a^{2} + 2 ab + b^{2} = (a + b)^{2}

(\frac{3}{2} p)^{2} + 2 \cdot \frac{3}{2} p \frac{1}{2} q + (\frac{1}{2} q)^{2} = (\frac{3}{2} p + \frac{1}{2} q)^{2}

= (\frac{3}{2} p + \frac{1}{2} q)^{2}

s im pl i f y \frac{2}{11}

s im pl i f y 1 + 4

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s im pl i f y 2 \cdot 1 0^{- 3}

f a c t or r^{2} + 2 rs + r