What is expand (x^2+sqrt(2))^{12} ?

The solution to expand (x^2+sqrt(2))^{12} is

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expand (x^2+sqrt(2))^{12}

expand

(x^{2} + 2)^{12}

x^{24} + 122 x^{22} + 132 x^{20} + 4402 x^{18} + 1980 x^{16} + 31682 x^{14} + 7392 x^{12} + 63362 x^{10} + 7920 x^{8} + 35202 x^{6} + 2112 x^{4} + 3842 x^{2} + 64

Solution steps

(x^{2} + 2)^{12}

Apply binomial theorem:

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

a = x^{2}, b = 2

= i = 0 \sum 12 (i 12) (x^{2})^{(12 - i)} (2)^{i}

Expand summation

= \frac{12 !}{0 ! ( 12 - 0 ) !} (x^{2})^{12} (2)^{0} + \frac{12 !}{1 ! ( 12 - 1 ) !} (x^{2})^{11} (2)^{1} + \frac{12 !}{2 ! ( 12 - 2 ) !} (x^{2})^{10} (2)^{2} + \frac{12 !}{3 ! ( 12 - 3 ) !} (x^{2})^{9} (2)^{3} + \frac{12 !}{4 ! ( 12 - 4 ) !} (x^{2})^{8} (2)^{4} + \frac{12 !}{5 ! ( 12 - 5 ) !} (x^{2})^{7} (2)^{5} + \frac{12 !}{6 ! ( 12 - 6 ) !} (x^{2})^{6} (2)^{6} + \frac{12 !}{7 ! ( 12 - 7 ) !} (x^{2})^{5} (2)^{7} + \frac{12 !}{8 ! ( 12 - 8 ) !} (x^{2})^{4} (2)^{8} + \frac{12 !}{9 ! ( 12 - 9 ) !} (x^{2})^{3} (2)^{9} + \frac{12 !}{10 ! ( 12 - 10 ) !} (x^{2})^{2} (2)^{10} + \frac{12 !}{11 ! ( 12 - 11 ) !} (x^{2})^{1} (2)^{11} + \frac{12 !}{12 ! ( 12 - 12 ) !} (x^{2})^{0} (2)^{12}

Simplify

\frac{12 !}{0 ! ( 12 - 0 ) !} (x^{2})^{12} (2)^{0} : x^{24}

Simplify

\frac{12 !}{1 ! ( 12 - 1 ) !} (x^{2})^{11} (2)^{1} : 122 x^{22}

Simplify

\frac{12 !}{2 ! ( 12 - 2 ) !} (x^{2})^{10} (2)^{2} : 132 x^{20}

Simplify

\frac{12 !}{3 ! ( 12 - 3 ) !} (x^{2})^{9} (2)^{3} : 4402 x^{18}

Simplify

\frac{12 !}{4 ! ( 12 - 4 ) !} (x^{2})^{8} (2)^{4} : 1980 x^{16}

Simplify

\frac{12 !}{5 ! ( 12 - 5 ) !} (x^{2})^{7} (2)^{5} : 31682 x^{14}

Simplify

\frac{12 !}{6 ! ( 12 - 6 ) !} (x^{2})^{6} (2)^{6} : 7392 x^{12}

Simplify

\frac{12 !}{7 ! ( 12 - 7 ) !} (x^{2})^{5} (2)^{7} : 63362 x^{10}

Simplify

\frac{12 !}{8 ! ( 12 - 8 ) !} (x^{2})^{4} (2)^{8} : 7920 x^{8}

Simplify

\frac{12 !}{9 ! ( 12 - 9 ) !} (x^{2})^{3} (2)^{9} : 35202 x^{6}

Simplify

\frac{12 !}{10 ! ( 12 - 10 ) !} (x^{2})^{2} (2)^{10} : 2112 x^{4}

Simplify

\frac{12 !}{11 ! ( 12 - 11 ) !} (x^{2})^{1} (2)^{11} : 3842 x^{2}

Simplify

\frac{12 !}{12 ! ( 12 - 12 ) !} (x^{2})^{0} (2)^{12} : 64

= x^{24} + 122 x^{22} + 132 x^{20} + 4402 x^{18} + 1980 x^{16} + 31682 x^{14} + 7392 x^{12} + 63362 x^{10} + 7920 x^{8} + 35202 x^{6} + 2112 x^{4} + 3842 x^{2} + 64

(x - 1)^{2} (e^{x} - 1)

\frac{- 4 s - 11}{( s + 2 ) ^{2}}

ln (5) (5 - x^{4})

\frac{3 x ^{3} - 4 x ^{2} + 5 x}{( 1 - x ) ^{2}}

\frac{( 2 - 3 s ) ( s - 1 )}{s ^{3}}

What is expand (x^2+sqrt(2))^{12} ?
The solution to expand (x^2+sqrt(2))^{12} is