erweitern ((15x+8y)^2)/(400)

Lösung

erweitern

\frac{( 15 x + 8 y ) ^{2}}{400}

\frac{9 x ^{2}}{16} + \frac{3 x y}{5} + \frac{4 y ^{2}}{25}

Schritte zur Lösung

\frac{( 15 x + 8 y ) ^{2}}{400}

(15 x + 8 y)^{2} = 225 x^{2} + 240 x y + 64 y^{2}

= \frac{225 x ^{2} + 240 x y + 64 y ^{2}}{400}

Wende Bruchregel an:

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

\frac{225 x ^{2} + 240 x y + 64 y ^{2}}{400} = \frac{225 x ^{2}}{400} + \frac{240 x y}{400} + \frac{64 y ^{2}}{400}

= \frac{225 x ^{2}}{400} + \frac{240 x y}{400} + \frac{64 y ^{2}}{400}

Streiche

\frac{225 x ^{2}}{400} : \frac{9 x ^{2}}{16}

= \frac{9 x ^{2}}{16} + \frac{240 x y}{400} + \frac{64 y ^{2}}{400}

Streiche

\frac{240 x y}{400} : \frac{3 x y}{5}

= \frac{9 x ^{2}}{16} + \frac{3 x y}{5} + \frac{64 y ^{2}}{400}

Streiche

\frac{64 y ^{2}}{400} : \frac{4 y ^{2}}{25}

= \frac{9 x ^{2}}{16} + \frac{3 x y}{5} + \frac{4 y ^{2}}{25}

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e x p an d (a + b) i + (c + d) j + (e + f) k