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Beliebt Algebra >

erweitern ((a+d+sqrt((a-d)^2+4bc))^2)/4

Lösung

erweitern

\frac{( a + d + ( a - d ) ^{2} + 4 b c ) ^{2}}{4}

Lösung

\frac{a ^{2}}{2} + \frac{a a ^{2} - 2 a d + d ^{2} + 4 b c}{2} + \frac{d a ^{2} - 2 a d + d ^{2} + 4 b c}{2} + \frac{d ^{2}}{2} + b c

Schritte zur Lösung

\frac{( a + d + ( a - d ) ^{2} + 4 b c ) ^{2}}{4}

(a + d + (a - d)^{2} + 4 b c)^{2} = 2 a^{2} + 2 a a^{2} - 2 a d + d^{2} + 4 b c + 2 d a^{2} - 2 a d + d^{2} + 4 b c + 2 d^{2} + 4 b c

= \frac{2 a ^{2} + 2 a a ^{2} - 2 a d + d ^{2} + 4 b c + 2 d a ^{2} - 2 a d + d ^{2} + 4 b c + 2 d ^{2} + 4 b c}{4}

Faktorisiere

2 a^{2} + 2 a a^{2} - 2 a d + d^{2} + 4 b c + 2 d a^{2} - 2 a d + d^{2} + 4 b c + 2 d^{2} + 4 b c : 2 (a^{2} + a a^{2} + d^{2} - 2 a d + 4 b c + d a^{2} + d^{2} - 2 a d + 4 b c + d^{2} + 2 b c)

= \frac{2 ( a ^{2} + a a ^{2} + d ^{2} - 2 a d + 4 b c + d a ^{2} + d ^{2} - 2 a d + 4 b c + d ^{2} + 2 b c )}{4}

Streiche die gemeinsamen Faktoren:

2

= \frac{a ^{2} + a a ^{2} - 2 a d + d ^{2} + 4 b c + d a ^{2} - 2 a d + d ^{2} + 4 b c + d ^{2} + 2 b c}{2}

Wende Bruchregel an:

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

\frac{a ^{2} + a a ^{2} - 2 a d + d ^{2} + 4 b c + d a ^{2} - 2 a d + d ^{2} + 4 b c + d ^{2} + 2 b c}{2} = \frac{a ^{2}}{2} + \frac{a a ^{2} - 2 a d + d ^{2} + 4 b c}{2} + \frac{d a ^{2} - 2 a d + d ^{2} + 4 b c}{2} + \frac{d ^{2}}{2} + \frac{2 b c}{2}

= \frac{a ^{2}}{2} + \frac{a a ^{2} - 2 a d + d ^{2} + 4 b c}{2} + \frac{d a ^{2} - 2 a d + d ^{2} + 4 b c}{2} + \frac{d ^{2}}{2} + \frac{2 b c}{2}

Teile die Zahlen:

\frac{2}{2} = 1

= \frac{a ^{2}}{2} + \frac{a a ^{2} - 2 a d + d ^{2} + 4 b c}{2} + \frac{d a ^{2} - 2 a d + d ^{2} + 4 b c}{2} + \frac{d ^{2}}{2} + b c

Beliebte Beispiele

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