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Popular >

expand (s+s')^{12}

Solution

expand

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

Solution

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}

Solution steps

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

Apply binomial theorem:

(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}

Expand summation

= \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}

Simplify

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

Simplify

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

Simplify

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

Simplify

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

Simplify

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

Simplify

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

Simplify

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

Simplify

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

Simplify

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

Simplify

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

Simplify

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

Simplify

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

Simplify

\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}

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5 (6 - 43)

Frequently Asked Questions (FAQ)

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