What is expand (sqrt(3)+sqrt(5))^{10} ?

The solution to expand (sqrt(3)+sqrt(5))^{10} is 483968+124960sqrt(15)

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expand (sqrt(3)+sqrt(5))^{10}

expand

(3 + 5)^{10}

483968 + 12496015

Solution steps

(3 + 5)^{10}

Apply binomial theorem:

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

a = 3, b = 5

= i = 0 \sum 10 (i 10) (3)^{(10 - i)} (5)^{i}

Expand summation

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

Simplify

\frac{10 !}{0 ! ( 10 - 0 ) !} (3)^{10} (5)^{0} : 243

Simplify

\frac{10 !}{1 ! ( 10 - 1 ) !} (3)^{9} (5)^{1} : 81015

Simplify

\frac{10 !}{2 ! ( 10 - 2 ) !} (3)^{8} (5)^{2} : 18225

Simplify

\frac{10 !}{3 ! ( 10 - 3 ) !} (3)^{7} (5)^{3} : 1620015

Simplify

\frac{10 !}{4 ! ( 10 - 4 ) !} (3)^{6} (5)^{4} : 141750

Simplify

\frac{10 !}{5 ! ( 10 - 5 ) !} (3)^{5} (5)^{5} : 5670015

Simplify

\frac{10 !}{6 ! ( 10 - 6 ) !} (3)^{4} (5)^{6} : 236250

Simplify

\frac{10 !}{7 ! ( 10 - 7 ) !} (3)^{3} (5)^{7} : 4500015

Simplify

\frac{10 !}{8 ! ( 10 - 8 ) !} (3)^{2} (5)^{8} : 84375

Simplify

\frac{10 !}{9 ! ( 10 - 9 ) !} (3)^{1} (5)^{9} : 625015

Simplify

\frac{10 !}{10 ! ( 10 - 10 ) !} (3)^{0} (5)^{10} : 3125

= 243 + 81015 + 18225 + 1620015 + 141750 + 5670015 + 236250 + 4500015 + 84375 + 625015 + 3125

243 + 81015 + 18225 + 1620015 + 141750 + 5670015 + 236250 + 4500015 + 84375 + 625015 + 3125 = 483968 + 12496015

= 483968 + 12496015

\frac{( - 12 x ^{2} - 324 )}{( x ^{2} + 9 ) ( x ^{2} + 81 )}

(e^{t} cos (t) + e^{t} sin (t)) d t

d y (y = 8 x^{3} + 7 5 x)

\frac{4}{x ( x - 4 )}

What is expand (sqrt(3)+sqrt(5))^{10} ?
The solution to expand (sqrt(3)+sqrt(5))^{10} is 483968+124960sqrt(15)