erweitern ((10+3x)/4)^2

Lösung

erweitern

(\frac{10 + 3 x}{4})^{2}

\frac{9 x ^{2}}{16} + \frac{15 x}{4} + \frac{25}{4}

Schritte zur Lösung

(\frac{10 + 3 x}{4})^{2}

Wende Exponentenregel an:

(\frac{a}{b})^{c} = \frac{a ^{c}}{b ^{c}}

= \frac{( 10 + 3 x ) ^{2}}{4 ^{2}}

(10 + 3 x)^{2} = 100 + 60 x + 9 x^{2}

= \frac{100 + 60 x + 9 x ^{2}}{4 ^{2}}

4^{2} = 16

= \frac{100 + 60 x + 9 x ^{2}}{16}

Wende Bruchregel an:

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

\frac{100 + 60 x + 9 x ^{2}}{16} = \frac{100}{16} + \frac{60 x}{16} + \frac{9 x ^{2}}{16}

= \frac{100}{16} + \frac{60 x}{16} + \frac{9 x ^{2}}{16}

Streiche

\frac{100}{16} : \frac{25}{4}

= \frac{25}{4} + \frac{60 x}{16} + \frac{9 x ^{2}}{16}

Streiche

\frac{60 x}{16} : \frac{15 x}{4}

= \frac{25}{4} + \frac{15 x}{4} + \frac{9 x ^{2}}{16}

Rewrite in standard form

= \frac{9 x ^{2}}{16} + \frac{15 x}{4} + \frac{25}{4}

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