de

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Beliebt Algebra >

erweitern (2x^6+(x^2)/5)^{10}

Lösung

erweitern

(2 x^{6} + \frac{x ^{2}}{5})^{10}

Lösung

1024 x^{60} + 1024 x^{56} + \frac{2304 x ^{52}}{5} + \frac{3072 x ^{48}}{25} + \frac{2688 x ^{44}}{125} + \frac{8064 x ^{40}}{3125} + \frac{672 x ^{36}}{3125} + \frac{192 x ^{32}}{15625} + \frac{36 x ^{28}}{78125} + \frac{4 x ^{24}}{390625} + \frac{x ^{20}}{9765625}

Schritte zur Lösung

(2 x^{6} + \frac{x ^{2}}{5})^{10}

Wende Binomialsetz an:

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

a = 2 x^{6}, b = \frac{x ^{2}}{5}

= i = 0 \sum 10 (i 10) (2 x^{6})^{(10 - i)} (\frac{x ^{2}}{5})^{i}

Erweitere Summation

= \frac{10 !}{0 ! ( 10 - 0 ) !} (2 x^{6})^{10} (\frac{x ^{2}}{5})^{0} + \frac{10 !}{1 ! ( 10 - 1 ) !} (2 x^{6})^{9} (\frac{x ^{2}}{5})^{1} + \frac{10 !}{2 ! ( 10 - 2 ) !} (2 x^{6})^{8} (\frac{x ^{2}}{5})^{2} + \frac{10 !}{3 ! ( 10 - 3 ) !} (2 x^{6})^{7} (\frac{x ^{2}}{5})^{3} + \frac{10 !}{4 ! ( 10 - 4 ) !} (2 x^{6})^{6} (\frac{x ^{2}}{5})^{4} + \frac{10 !}{5 ! ( 10 - 5 ) !} (2 x^{6})^{5} (\frac{x ^{2}}{5})^{5} + \frac{10 !}{6 ! ( 10 - 6 ) !} (2 x^{6})^{4} (\frac{x ^{2}}{5})^{6} + \frac{10 !}{7 ! ( 10 - 7 ) !} (2 x^{6})^{3} (\frac{x ^{2}}{5})^{7} + \frac{10 !}{8 ! ( 10 - 8 ) !} (2 x^{6})^{2} (\frac{x ^{2}}{5})^{8} + \frac{10 !}{9 ! ( 10 - 9 ) !} (2 x^{6})^{1} (\frac{x ^{2}}{5})^{9} + \frac{10 !}{10 ! ( 10 - 10 ) !} (2 x^{6})^{0} (\frac{x ^{2}}{5})^{10}

Vereinfache

\frac{10 !}{0 ! ( 10 - 0 ) !} (2 x^{6})^{10} (\frac{x ^{2}}{5})^{0} : 1024 x^{60}

Vereinfache

\frac{10 !}{1 ! ( 10 - 1 ) !} (2 x^{6})^{9} (\frac{x ^{2}}{5})^{1} : 1024 x^{56}

Vereinfache

\frac{10 !}{2 ! ( 10 - 2 ) !} (2 x^{6})^{8} (\frac{x ^{2}}{5})^{2} : \frac{2304 x ^{52}}{5}

Vereinfache

\frac{10 !}{3 ! ( 10 - 3 ) !} (2 x^{6})^{7} (\frac{x ^{2}}{5})^{3} : \frac{3072 x ^{48}}{25}

Vereinfache

\frac{10 !}{4 ! ( 10 - 4 ) !} (2 x^{6})^{6} (\frac{x ^{2}}{5})^{4} : \frac{2688 x ^{44}}{125}

Vereinfache

\frac{10 !}{5 ! ( 10 - 5 ) !} (2 x^{6})^{5} (\frac{x ^{2}}{5})^{5} : \frac{8064 x ^{40}}{3125}

Vereinfache

\frac{10 !}{6 ! ( 10 - 6 ) !} (2 x^{6})^{4} (\frac{x ^{2}}{5})^{6} : \frac{672 x ^{36}}{3125}

Vereinfache

\frac{10 !}{7 ! ( 10 - 7 ) !} (2 x^{6})^{3} (\frac{x ^{2}}{5})^{7} : \frac{192 x ^{32}}{15625}

Vereinfache

\frac{10 !}{8 ! ( 10 - 8 ) !} (2 x^{6})^{2} (\frac{x ^{2}}{5})^{8} : \frac{36 x ^{28}}{78125}

Vereinfache

\frac{10 !}{9 ! ( 10 - 9 ) !} (2 x^{6})^{1} (\frac{x ^{2}}{5})^{9} : \frac{4 x ^{24}}{390625}

Vereinfache

\frac{10 !}{10 ! ( 10 - 10 ) !} (2 x^{6})^{0} (\frac{x ^{2}}{5})^{10} : \frac{x ^{20}}{9765625}

= 1024 x^{60} + 1024 x^{56} + \frac{2304 x ^{52}}{5} + \frac{3072 x ^{48}}{25} + \frac{2688 x ^{44}}{125} + \frac{8064 x ^{40}}{3125} + \frac{672 x ^{36}}{3125} + \frac{192 x ^{32}}{15625} + \frac{36 x ^{28}}{78125} + \frac{4 x ^{24}}{390625} + \frac{x ^{20}}{9765625}

Beliebte Beispiele

vereinfachen 2(1+sqrt(5))

s im pl i f y 2 (1 + 5)

erweitern (2(-x^2+4))/((x^2+4)^2)

e x p an d \frac{2 ( - x ^{2} + 4 )}{( x ^{2} + 4 ) ^{2}}

erweitern (e^{2x}+e^{-2x})^2

e x p an d (e^{2 x} + e^{- 2 x})^{2}

erweitern sqrt((x+h)^2-3)

e x p an d (x + h)^{2} - 3

erweitern ((m-1)+1)^n

e x p an d ((m - 1) + 1)^{n}