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Popular >

expand (a+b)^{17}

Solution

expand

(a + b)^{17}

Solution

a^{17} + 17 a^{16} b + 136 a^{15} b^{2} + 680 a^{14} b^{3} + 2380 a^{13} b^{4} + 6188 a^{12} b^{5} + 12376 a^{11} b^{6} + 19448 a^{10} b^{7} + 24310 a^{9} b^{8} + 24310 a^{8} b^{9} + 19448 a^{7} b^{10} + 12376 a^{6} b^{11} + 6188 a^{5} b^{12} + 2380 a^{4} b^{13} + 680 a^{3} b^{14} + 136 a^{2} b^{15} + 17 a b^{16} + b^{17}

Solution steps

(a + b)^{17}

Apply binomial theorem:

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

a = a, b = b

= i = 0 \sum 17 (i 17) a^{(17 - i)} b^{i}

Expand summation

= \frac{17 !}{0 ! ( 17 - 0 ) !} a^{17} b^{0} + \frac{17 !}{1 ! ( 17 - 1 ) !} a^{16} b^{1} + \frac{17 !}{2 ! ( 17 - 2 ) !} a^{15} b^{2} + \frac{17 !}{3 ! ( 17 - 3 ) !} a^{14} b^{3} + \frac{17 !}{4 ! ( 17 - 4 ) !} a^{13} b^{4} + \frac{17 !}{5 ! ( 17 - 5 ) !} a^{12} b^{5} + \frac{17 !}{6 ! ( 17 - 6 ) !} a^{11} b^{6} + \frac{17 !}{7 ! ( 17 - 7 ) !} a^{10} b^{7} + \frac{17 !}{8 ! ( 17 - 8 ) !} a^{9} b^{8} + \frac{17 !}{9 ! ( 17 - 9 ) !} a^{8} b^{9} + \frac{17 !}{10 ! ( 17 - 10 ) !} a^{7} b^{10} + \frac{17 !}{11 ! ( 17 - 11 ) !} a^{6} b^{11} + \frac{17 !}{12 ! ( 17 - 12 ) !} a^{5} b^{12} + \frac{17 !}{13 ! ( 17 - 13 ) !} a^{4} b^{13} + \frac{17 !}{14 ! ( 17 - 14 ) !} a^{3} b^{14} + \frac{17 !}{15 ! ( 17 - 15 ) !} a^{2} b^{15} + \frac{17 !}{16 ! ( 17 - 16 ) !} a^{1} b^{16} + \frac{17 !}{17 ! ( 17 - 17 ) !} a^{0} b^{17}

Simplify

\frac{17 !}{0 ! ( 17 - 0 ) !} a^{17} b^{0} : a^{17}

Simplify

\frac{17 !}{1 ! ( 17 - 1 ) !} a^{16} b^{1} : 17 a^{16} b

Simplify

\frac{17 !}{2 ! ( 17 - 2 ) !} a^{15} b^{2} : 136 a^{15} b^{2}

Simplify

\frac{17 !}{3 ! ( 17 - 3 ) !} a^{14} b^{3} : 680 a^{14} b^{3}

Simplify

\frac{17 !}{4 ! ( 17 - 4 ) !} a^{13} b^{4} : 2380 a^{13} b^{4}

Simplify

\frac{17 !}{5 ! ( 17 - 5 ) !} a^{12} b^{5} : 6188 a^{12} b^{5}

Simplify

\frac{17 !}{6 ! ( 17 - 6 ) !} a^{11} b^{6} : 12376 a^{11} b^{6}

Simplify

\frac{17 !}{7 ! ( 17 - 7 ) !} a^{10} b^{7} : 19448 a^{10} b^{7}

Simplify

\frac{17 !}{8 ! ( 17 - 8 ) !} a^{9} b^{8} : 24310 a^{9} b^{8}

Simplify

\frac{17 !}{9 ! ( 17 - 9 ) !} a^{8} b^{9} : 24310 a^{8} b^{9}

Simplify

\frac{17 !}{10 ! ( 17 - 10 ) !} a^{7} b^{10} : 19448 a^{7} b^{10}

Simplify

\frac{17 !}{11 ! ( 17 - 11 ) !} a^{6} b^{11} : 12376 a^{6} b^{11}

Simplify

\frac{17 !}{12 ! ( 17 - 12 ) !} a^{5} b^{12} : 6188 a^{5} b^{12}

Simplify

\frac{17 !}{13 ! ( 17 - 13 ) !} a^{4} b^{13} : 2380 a^{4} b^{13}

Simplify

\frac{17 !}{14 ! ( 17 - 14 ) !} a^{3} b^{14} : 680 a^{3} b^{14}

Simplify

\frac{17 !}{15 ! ( 17 - 15 ) !} a^{2} b^{15} : 136 a^{2} b^{15}

Simplify

\frac{17 !}{16 ! ( 17 - 16 ) !} a^{1} b^{16} : 17 a b^{16}

Simplify

\frac{17 !}{17 ! ( 17 - 17 ) !} a^{0} b^{17} : b^{17}

= a^{17} + 17 a^{16} b + 136 a^{15} b^{2} + 680 a^{14} b^{3} + 2380 a^{13} b^{4} + 6188 a^{12} b^{5} + 12376 a^{11} b^{6} + 19448 a^{10} b^{7} + 24310 a^{9} b^{8} + 24310 a^{8} b^{9} + 19448 a^{7} b^{10} + 12376 a^{6} b^{11} + 6188 a^{5} b^{12} + 2380 a^{4} b^{13} + 680 a^{3} b^{14} + 136 a^{2} b^{15} + 17 a b^{16} + b^{17}

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Frequently Asked Questions (FAQ)

What is expand (a+b)^{17} ?
The solution to expand (a+b)^{17} is