What is expand (2+sqrt(3))^8 ?

The solution to expand (2+sqrt(3))^8 is 18817+10864sqrt(3)

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expand (2+sqrt(3))^8

expand

(2 + 3)^{8}

18817 + 108643

Decimal Notation

37633.99997 \dots

Solution steps

(2 + 3)^{8}

Apply binomial theorem:

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

a = 2, b = 3

= i = 0 \sum 8 (i 8) \cdot 2^{(8 - i)} (3)^{i}

Expand summation

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

Simplify

\frac{8 !}{0 ! ( 8 - 0 ) !} \cdot 2^{8} (3)^{0} : 256

Simplify

\frac{8 !}{1 ! ( 8 - 1 ) !} \cdot 2^{7} (3)^{1} : 10243

Simplify

\frac{8 !}{2 ! ( 8 - 2 ) !} \cdot 2^{6} (3)^{2} : 5376

Simplify

\frac{8 !}{3 ! ( 8 - 3 ) !} \cdot 2^{5} (3)^{3} : 53763

Simplify

\frac{8 !}{4 ! ( 8 - 4 ) !} \cdot 2^{4} (3)^{4} : 10080

Simplify

\frac{8 !}{5 ! ( 8 - 5 ) !} \cdot 2^{3} (3)^{5} : 40323

Simplify

\frac{8 !}{6 ! ( 8 - 6 ) !} \cdot 2^{2} (3)^{6} : 3024

Simplify

\frac{8 !}{7 ! ( 8 - 7 ) !} \cdot 2^{1} (3)^{7} : 4323

Simplify

\frac{8 !}{8 ! ( 8 - 8 ) !} \cdot 2^{0} (3)^{8} : 81

= 256 + 10243 + 5376 + 53763 + 10080 + 40323 + 3024 + 4323 + 81

256 + 10243 + 5376 + 53763 + 10080 + 40323 + 3024 + 4323 + 81 = 18817 + 108643

= 18817 + 108643

\frac{2 x}{( x + 1 ) ( x ^{2} + 1 ) ^{2}}

(x^{2} - \frac{1}{x ^{4}})^{6}

ln^{2} (x - 2) (e^{x - 3} - 1) sin (\frac{π x}{3})

\frac{1}{s ^{2} ( s + 4 )}

\frac{( 3 x + 1 ) ^{3}}{3}

What is expand (2+sqrt(3))^8 ?
The solution to expand (2+sqrt(3))^8 is 18817+10864sqrt(3)