erweitern (k^2+3k+3)^2 1/4

Lösung

erweitern

(k^{2} + 3 k + 3)^{2} \frac{1}{4}

\frac{k ^{4}}{4} + \frac{15 k ^{2}}{4} + \frac{9}{4} + \frac{3 k ^{3}}{2} + \frac{9 k}{2}

Schritte zur Lösung

(k^{2} + 3 k + 3)^{2} \frac{1}{4}

(k^{2} + 3 k + 3)^{2} = k^{4} + 6 k^{3} + 15 k^{2} + 18 k + 9

= \frac{1}{4} (k^{4} + 6 k^{3} + 15 k^{2} + 18 k + 9)

= \frac{1}{4} (k^{4} + 6 k^{3} + 15 k^{2} + 18 k + 9)

Setze Klammern

= \frac{1}{4} k^{4} + \frac{1}{4} \cdot 6 k^{3} + \frac{1}{4} \cdot 15 k^{2} + \frac{1}{4} \cdot 18 k + \frac{1}{4} \cdot 9

= \frac{1}{4} k^{4} + 6 \cdot \frac{1}{4} k^{3} + 15 \cdot \frac{1}{4} k^{2} + 18 \cdot \frac{1}{4} k + 9 \cdot \frac{1}{4}

Vereinfache

\frac{1}{4} k^{4} + 6 \cdot \frac{1}{4} k^{3} + 15 \cdot \frac{1}{4} k^{2} + 18 \cdot \frac{1}{4} k + 9 \cdot \frac{1}{4} : \frac{k ^{4} + 15 k ^{2} + 9}{4} + \frac{3 k ^{3} + 9 k}{2}

= \frac{k ^{4} + 15 k ^{2} + 9}{4} + \frac{3 k ^{3} + 9 k}{2}

Wende Bruchregel an:

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

\frac{k ^{4} + 15 k ^{2} + 9}{4} = \frac{k ^{4}}{4} + \frac{15 k ^{2}}{4} + \frac{9}{4}

= \frac{k ^{4}}{4} + \frac{15 k ^{2}}{4} + \frac{9}{4} + \frac{3 k ^{3} + 9 k}{2}

Wende Bruchregel an:

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

\frac{3 k ^{3} + 9 k}{2} = \frac{3 k ^{3}}{2} + \frac{9 k}{2}

= \frac{k ^{4}}{4} + \frac{15 k ^{2}}{4} + \frac{9}{4} + \frac{3 k ^{3}}{2} + \frac{9 k}{2}

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