erweitern ((((2y+3)/5))/(2))^2

Lösung

erweitern

(\frac{( \frac{2 y + 3}{5} )}{2})^{2}

\frac{y ^{2}}{25} + \frac{3 y}{25} + \frac{9}{100}

Schritte zur Lösung

(\frac{\frac{2 y + 3}{5}}{2})^{2}

\frac{\frac{2 y + 3}{5}}{2} = \frac{2 y + 3}{10}

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

Wende Exponentenregel an:

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

= \frac{( 2 y + 3 ) ^{2}}{1 0 ^{2}}

(2 y + 3)^{2} = 4 y^{2} + 12 y + 9

= \frac{4 y ^{2} + 12 y + 9}{1 0 ^{2}}

1 0^{2} = 100

= \frac{4 y ^{2} + 12 y + 9}{100}

Wende Bruchregel an:

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

\frac{4 y ^{2} + 12 y + 9}{100} = \frac{4 y ^{2}}{100} + \frac{12 y}{100} + \frac{9}{100}

= \frac{4 y ^{2}}{100} + \frac{12 y}{100} + \frac{9}{100}

Streiche

\frac{4 y ^{2}}{100} : \frac{y ^{2}}{25}

= \frac{y ^{2}}{25} + \frac{12 y}{100} + \frac{9}{100}

Streiche

\frac{12 y}{100} : \frac{3 y}{25}

= \frac{y ^{2}}{25} + \frac{3 y}{25} + \frac{9}{100}

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s im pl i f y sin^{2} (t) (t) (7 - t^{2})

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