What is expand (a^{2/3}+a^{1/3})^{25} ?

The solution to expand (a^{2/3}+a^{1/3})^{25} is

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expand (a^{2/3}+a^{1/3})^{25}

Solution

expand

(a^{\frac{2}{3}} + a^{\frac{1}{3}})^{25}

Solution

a^{\frac{50}{3}} + 25 a^{\frac{49}{3}} + 300 a^{16} + 2300 a^{\frac{47}{3}} + 12650 a^{\frac{46}{3}} + 53130 a^{15} + 177100 a^{\frac{44}{3}} + 480700 a^{\frac{43}{3}} + 1081575 a^{14} + 2042975 a^{\frac{41}{3}} + 3268760 a^{\frac{40}{3}} + 4457400 a^{13} + 5200300 a^{\frac{38}{3}} + 5200300 a^{\frac{37}{3}} + 4457400 a^{12} + 3268760 a^{\frac{35}{3}} + 2042975 a^{\frac{34}{3}} + 1081575 a^{11} + 480700 a^{\frac{32}{3}} + 177100 a^{\frac{31}{3}} + 53130 a^{10} + 12650 a^{\frac{29}{3}} + 2300 a^{\frac{28}{3}} + 300 a^{9} + 25 a^{\frac{26}{3}} + a^{\frac{25}{3}}

Solution steps

(a^{\frac{2}{3}} + a^{\frac{1}{3}})^{25}

Apply binomial theorem:

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

a = a^{\frac{2}{3}}, b = a^{\frac{1}{3}}

= i = 0 \sum 25 (i 25) (a^{\frac{2}{3}})^{(25 - i)} (a^{\frac{1}{3}})^{i}

Expand summation

Simplify

\frac{25 !}{0 ! ( 25 - 0 ) !} (a^{\frac{2}{3}})^{25} (a^{\frac{1}{3}})^{0} : a^{\frac{50}{3}}

Simplify

\frac{25 !}{1 ! ( 25 - 1 ) !} (a^{\frac{2}{3}})^{24} (a^{\frac{1}{3}})^{1} : 25 a^{\frac{49}{3}}

Simplify

\frac{25 !}{2 ! ( 25 - 2 ) !} (a^{\frac{2}{3}})^{23} (a^{\frac{1}{3}})^{2} : 300 a^{16}

Simplify

\frac{25 !}{3 ! ( 25 - 3 ) !} (a^{\frac{2}{3}})^{22} (a^{\frac{1}{3}})^{3} : 2300 a^{\frac{47}{3}}

Simplify

\frac{25 !}{4 ! ( 25 - 4 ) !} (a^{\frac{2}{3}})^{21} (a^{\frac{1}{3}})^{4} : 12650 a^{\frac{46}{3}}

Simplify

\frac{25 !}{5 ! ( 25 - 5 ) !} (a^{\frac{2}{3}})^{20} (a^{\frac{1}{3}})^{5} : 53130 a^{15}

Simplify

\frac{25 !}{6 ! ( 25 - 6 ) !} (a^{\frac{2}{3}})^{19} (a^{\frac{1}{3}})^{6} : 177100 a^{\frac{44}{3}}

Simplify

\frac{25 !}{7 ! ( 25 - 7 ) !} (a^{\frac{2}{3}})^{18} (a^{\frac{1}{3}})^{7} : 480700 a^{\frac{43}{3}}

Simplify

\frac{25 !}{8 ! ( 25 - 8 ) !} (a^{\frac{2}{3}})^{17} (a^{\frac{1}{3}})^{8} : 1081575 a^{14}

Simplify

\frac{25 !}{9 ! ( 25 - 9 ) !} (a^{\frac{2}{3}})^{16} (a^{\frac{1}{3}})^{9} : 2042975 a^{\frac{41}{3}}

Simplify

\frac{25 !}{10 ! ( 25 - 10 ) !} (a^{\frac{2}{3}})^{15} (a^{\frac{1}{3}})^{10} : 3268760 a^{\frac{40}{3}}

Simplify

\frac{25 !}{11 ! ( 25 - 11 ) !} (a^{\frac{2}{3}})^{14} (a^{\frac{1}{3}})^{11} : 4457400 a^{13}

Simplify

\frac{25 !}{12 ! ( 25 - 12 ) !} (a^{\frac{2}{3}})^{13} (a^{\frac{1}{3}})^{12} : 5200300 a^{\frac{38}{3}}

Simplify

\frac{25 !}{13 ! ( 25 - 13 ) !} (a^{\frac{2}{3}})^{12} (a^{\frac{1}{3}})^{13} : 5200300 a^{\frac{37}{3}}

Simplify

\frac{25 !}{14 ! ( 25 - 14 ) !} (a^{\frac{2}{3}})^{11} (a^{\frac{1}{3}})^{14} : 4457400 a^{12}

Simplify

\frac{25 !}{15 ! ( 25 - 15 ) !} (a^{\frac{2}{3}})^{10} (a^{\frac{1}{3}})^{15} : 3268760 a^{\frac{35}{3}}

Simplify

\frac{25 !}{16 ! ( 25 - 16 ) !} (a^{\frac{2}{3}})^{9} (a^{\frac{1}{3}})^{16} : 2042975 a^{\frac{34}{3}}

Simplify

\frac{25 !}{17 ! ( 25 - 17 ) !} (a^{\frac{2}{3}})^{8} (a^{\frac{1}{3}})^{17} : 1081575 a^{11}

Simplify

\frac{25 !}{18 ! ( 25 - 18 ) !} (a^{\frac{2}{3}})^{7} (a^{\frac{1}{3}})^{18} : 480700 a^{\frac{32}{3}}

Simplify

\frac{25 !}{19 ! ( 25 - 19 ) !} (a^{\frac{2}{3}})^{6} (a^{\frac{1}{3}})^{19} : 177100 a^{\frac{31}{3}}

Simplify

\frac{25 !}{20 ! ( 25 - 20 ) !} (a^{\frac{2}{3}})^{5} (a^{\frac{1}{3}})^{20} : 53130 a^{10}

Simplify

\frac{25 !}{21 ! ( 25 - 21 ) !} (a^{\frac{2}{3}})^{4} (a^{\frac{1}{3}})^{21} : 12650 a^{\frac{29}{3}}

Simplify

\frac{25 !}{22 ! ( 25 - 22 ) !} (a^{\frac{2}{3}})^{3} (a^{\frac{1}{3}})^{22} : 2300 a^{\frac{28}{3}}

Simplify

\frac{25 !}{23 ! ( 25 - 23 ) !} (a^{\frac{2}{3}})^{2} (a^{\frac{1}{3}})^{23} : 300 a^{9}

Simplify

\frac{25 !}{24 ! ( 25 - 24 ) !} (a^{\frac{2}{3}})^{1} (a^{\frac{1}{3}})^{24} : 25 a^{\frac{26}{3}}

Simplify

\frac{25 !}{25 ! ( 25 - 25 ) !} (a^{\frac{2}{3}})^{0} (a^{\frac{1}{3}})^{25} : a^{\frac{25}{3}}

= a^{\frac{50}{3}} + 25 a^{\frac{49}{3}} + 300 a^{16} + 2300 a^{\frac{47}{3}} + 12650 a^{\frac{46}{3}} + 53130 a^{15} + 177100 a^{\frac{44}{3}} + 480700 a^{\frac{43}{3}} + 1081575 a^{14} + 2042975 a^{\frac{41}{3}} + 3268760 a^{\frac{40}{3}} + 4457400 a^{13} + 5200300 a^{\frac{38}{3}} + 5200300 a^{\frac{37}{3}} + 4457400 a^{12} + 3268760 a^{\frac{35}{3}} + 2042975 a^{\frac{34}{3}} + 1081575 a^{11} + 480700 a^{\frac{32}{3}} + 177100 a^{\frac{31}{3}} + 53130 a^{10} + 12650 a^{\frac{29}{3}} + 2300 a^{\frac{28}{3}} + 300 a^{9} + 25 a^{\frac{26}{3}} + a^{\frac{25}{3}}

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Frequently Asked Questions (FAQ)

What is expand (a^{2/3}+a^{1/3})^{25} ?
The solution to expand (a^{2/3}+a^{1/3})^{25} is