it

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popolare Algebra >

espandere (s+s')^{12}

Soluzione

espandere

(s + s^{'})^{12}

Soluzione

s^{12} + 12 s^{11} s' + 66 s^{10} (s')^{2} + 220 s^{9} (s')^{3} + 495 s^{8} (s')^{4} + 792 s^{7} (s')^{5} + 924 s^{6} (s')^{6} + 792 s^{5} (s')^{7} + 495 s^{4} (s')^{8} + 220 s^{3} (s')^{9} + 66 s^{2} (s')^{10} + 12 s (s')^{11} + (s')^{12}

Fasi della soluzione

(s + s^{'})^{12}

Applicare il teorema binomiale:

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

a = s, b = s^{'}

= i = 0 \sum 12 (i 12) s^{(12 - i)} (s^{^{'}})^{i}

Espandere la sommatoria

= \frac{12 !}{0 ! ( 12 - 0 ) !} s^{12} (s^{'})^{0} + \frac{12 !}{1 ! ( 12 - 1 ) !} s^{11} (s^{'})^{1} + \frac{12 !}{2 ! ( 12 - 2 ) !} s^{10} (s^{'})^{2} + \frac{12 !}{3 ! ( 12 - 3 ) !} s^{9} (s^{'})^{3} + \frac{12 !}{4 ! ( 12 - 4 ) !} s^{8} (s^{'})^{4} + \frac{12 !}{5 ! ( 12 - 5 ) !} s^{7} (s^{'})^{5} + \frac{12 !}{6 ! ( 12 - 6 ) !} s^{6} (s^{'})^{6} + \frac{12 !}{7 ! ( 12 - 7 ) !} s^{5} (s^{'})^{7} + \frac{12 !}{8 ! ( 12 - 8 ) !} s^{4} (s^{'})^{8} + \frac{12 !}{9 ! ( 12 - 9 ) !} s^{3} (s^{'})^{9} + \frac{12 !}{10 ! ( 12 - 10 ) !} s^{2} (s^{'})^{10} + \frac{12 !}{11 ! ( 12 - 11 ) !} s^{1} (s^{'})^{11} + \frac{12 !}{12 ! ( 12 - 12 ) !} s^{0} (s^{'})^{12}

Semplifica

\frac{12 !}{0 ! ( 12 - 0 ) !} s^{12} (s^{'})^{0} : s^{12}

Semplifica

\frac{12 !}{1 ! ( 12 - 1 ) !} s^{11} (s^{'})^{1} : 12 s^{11} s^{'}

Semplifica

\frac{12 !}{2 ! ( 12 - 2 ) !} s^{10} (s^{'})^{2} : 66 s^{10} (s^{'})^{2}

Semplifica

\frac{12 !}{3 ! ( 12 - 3 ) !} s^{9} (s^{'})^{3} : 220 s^{9} (s^{'})^{3}

Semplifica

\frac{12 !}{4 ! ( 12 - 4 ) !} s^{8} (s^{'})^{4} : 495 s^{8} (s^{'})^{4}

Semplifica

\frac{12 !}{5 ! ( 12 - 5 ) !} s^{7} (s^{'})^{5} : 792 s^{7} (s^{'})^{5}

Semplifica

\frac{12 !}{6 ! ( 12 - 6 ) !} s^{6} (s^{'})^{6} : 924 s^{6} (s^{'})^{6}

Semplifica

\frac{12 !}{7 ! ( 12 - 7 ) !} s^{5} (s^{'})^{7} : 792 s^{5} (s^{'})^{7}

Semplifica

\frac{12 !}{8 ! ( 12 - 8 ) !} s^{4} (s^{'})^{8} : 495 s^{4} (s^{'})^{8}

Semplifica

\frac{12 !}{9 ! ( 12 - 9 ) !} s^{3} (s^{'})^{9} : 220 s^{3} (s^{'})^{9}

Semplifica

\frac{12 !}{10 ! ( 12 - 10 ) !} s^{2} (s^{'})^{10} : 66 s^{2} (s^{'})^{10}

Semplifica

\frac{12 !}{11 ! ( 12 - 11 ) !} s^{1} (s^{'})^{11} : 12 s (s^{'})^{11}

Semplifica

\frac{12 !}{12 ! ( 12 - 12 ) !} s^{0} (s^{'})^{12} : (s^{'})^{12}

= s^{12} + 12 s^{11} s^{^{'}} + 66 s^{10} (s^{^{'}})^{2} + 220 s^{9} (s^{^{'}})^{3} + 495 s^{8} (s^{^{'}})^{4} + 792 s^{7} (s^{^{'}})^{5} + 924 s^{6} (s^{^{'}})^{6} + 792 s^{5} (s^{^{'}})^{7} + 495 s^{4} (s^{^{'}})^{8} + 220 s^{3} (s^{^{'}})^{9} + 66 s^{2} (s^{^{'}})^{10} + 12 s (s^{^{'}})^{11} + (s^{^{'}})^{12}

Esempi popolari

espandere (2x)/((s+1)(s^2+1)^2)

e x p an d \frac{2 x}{( s + 1 ) ( s ^{2} + 1 ) ^{2}}

espandere (x-x^2)e^x

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

espandere x/((x^2+3)^2)

e x p an d \frac{x}{( x ^{2} + 3 ) ^{2}}

espandere 10(x/2-1/5 =y)

e x p an d 10 (\frac{x}{2} - \frac{1}{5} = y)

espandere sqrt(5)(6-4sqrt(3))

e x p an d 5 (6 - 43)