erweitern (x^2+4z^2)^5

Lösung

erweitern

(x^{2} + 4 z^{2})^{5}

x^{10} + 20 x^{8} z^{2} + 160 x^{6} z^{4} + 640 x^{4} z^{6} + 1280 x^{2} z^{8} + 1024 z^{10}

Schritte zur Lösung

(x^{2} + 4 z^{2})^{5}

Wende Binomialsetz an:

(a + b)^{n} = i = 0 \sum n (i n) a^{(n - i)} b^{i}

a = x^{2}, b = 4 z^{2}

= i = 0 \sum 5 (i 5) (x^{2})^{(5 - i)} (4 z^{2})^{i}

Erweitere Summation

= \frac{5 !}{0 ! ( 5 - 0 ) !} (x^{2})^{5} (4 z^{2})^{0} + \frac{5 !}{1 ! ( 5 - 1 ) !} (x^{2})^{4} (4 z^{2})^{1} + \frac{5 !}{2 ! ( 5 - 2 ) !} (x^{2})^{3} (4 z^{2})^{2} + \frac{5 !}{3 ! ( 5 - 3 ) !} (x^{2})^{2} (4 z^{2})^{3} + \frac{5 !}{4 ! ( 5 - 4 ) !} (x^{2})^{1} (4 z^{2})^{4} + \frac{5 !}{5 ! ( 5 - 5 ) !} (x^{2})^{0} (4 z^{2})^{5}

Vereinfache

\frac{5 !}{0 ! ( 5 - 0 ) !} (x^{2})^{5} (4 z^{2})^{0} : x^{10}

Vereinfache

\frac{5 !}{1 ! ( 5 - 1 ) !} (x^{2})^{4} (4 z^{2})^{1} : 20 x^{8} z^{2}

Vereinfache

\frac{5 !}{2 ! ( 5 - 2 ) !} (x^{2})^{3} (4 z^{2})^{2} : 160 x^{6} z^{4}

Vereinfache

\frac{5 !}{3 ! ( 5 - 3 ) !} (x^{2})^{2} (4 z^{2})^{3} : 640 x^{4} z^{6}

Vereinfache

\frac{5 !}{4 ! ( 5 - 4 ) !} (x^{2})^{1} (4 z^{2})^{4} : 1280 x^{2} z^{8}

Vereinfache

\frac{5 !}{5 ! ( 5 - 5 ) !} (x^{2})^{0} (4 z^{2})^{5} : 1024 z^{10}

= x^{10} + 20 x^{8} z^{2} + 160 x^{6} z^{4} + 640 x^{4} z^{6} + 1280 x^{2} z^{8} + 1024 z^{10}

s im pl i f y \frac{5}{6} - \frac{1}{6 x}

s im pl i f y 2 (x - 1)^{2} - 2

s im pl i f y lo g_{a} (8)

- 1 \frac{1}{5}

s im pl i f y lo g_{2} (0.02)