What is expand (2x^6+(x^2)/4)^{10} ?

The solution to expand (2x^6+(x^2)/4)^{10} is

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expand (2x^6+(x^2)/4)^{10}

expand

(2 x^{6} + \frac{x ^{2}}{4})^{10}

1024 x^{60} + 1280 x^{56} + 720 x^{52} + 240 x^{48} + \frac{105 x ^{44}}{2} + \frac{63 x ^{40}}{8} + \frac{105 x ^{36}}{128} + \frac{15 x ^{32}}{256} + \frac{45 x ^{28}}{16384} + \frac{5 x ^{24}}{65536} + \frac{x ^{20}}{1048576}

Solution steps

(2 x^{6} + \frac{x ^{2}}{4})^{10}

Apply binomial theorem:

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

a = 2 x^{6}, b = \frac{x ^{2}}{4}

= i = 0 \sum 10 (i 10) (2 x^{6})^{(10 - i)} (\frac{x ^{2}}{4})^{i}

Expand summation

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

Simplify

\frac{10 !}{0 ! ( 10 - 0 ) !} (2 x^{6})^{10} (\frac{x ^{2}}{4})^{0} : 1024 x^{60}

Simplify

\frac{10 !}{1 ! ( 10 - 1 ) !} (2 x^{6})^{9} (\frac{x ^{2}}{4})^{1} : 1280 x^{56}

Simplify

\frac{10 !}{2 ! ( 10 - 2 ) !} (2 x^{6})^{8} (\frac{x ^{2}}{4})^{2} : 720 x^{52}

Simplify

\frac{10 !}{3 ! ( 10 - 3 ) !} (2 x^{6})^{7} (\frac{x ^{2}}{4})^{3} : 240 x^{48}

Simplify

\frac{10 !}{4 ! ( 10 - 4 ) !} (2 x^{6})^{6} (\frac{x ^{2}}{4})^{4} : \frac{105 x ^{44}}{2}

Simplify

\frac{10 !}{5 ! ( 10 - 5 ) !} (2 x^{6})^{5} (\frac{x ^{2}}{4})^{5} : \frac{63 x ^{40}}{8}

Simplify

\frac{10 !}{6 ! ( 10 - 6 ) !} (2 x^{6})^{4} (\frac{x ^{2}}{4})^{6} : \frac{105 x ^{36}}{128}

Simplify

\frac{10 !}{7 ! ( 10 - 7 ) !} (2 x^{6})^{3} (\frac{x ^{2}}{4})^{7} : \frac{15 x ^{32}}{256}

Simplify

\frac{10 !}{8 ! ( 10 - 8 ) !} (2 x^{6})^{2} (\frac{x ^{2}}{4})^{8} : \frac{45 x ^{28}}{16384}

Simplify

\frac{10 !}{9 ! ( 10 - 9 ) !} (2 x^{6})^{1} (\frac{x ^{2}}{4})^{9} : \frac{5 x ^{24}}{65536}

Simplify

\frac{10 !}{10 ! ( 10 - 10 ) !} (2 x^{6})^{0} (\frac{x ^{2}}{4})^{10} : \frac{x ^{20}}{1048576}

= 1024 x^{60} + 1280 x^{56} + 720 x^{52} + 240 x^{48} + \frac{105 x ^{44}}{2} + \frac{63 x ^{40}}{8} + \frac{105 x ^{36}}{128} + \frac{15 x ^{32}}{256} + \frac{45 x ^{28}}{16384} + \frac{5 x ^{24}}{65536} + \frac{x ^{20}}{1048576}

(5 x^{3} + 3 x^{2}) (- 4 x + 5)^{10}

(q - \frac{3}{4}) (q + \frac{1}{4})

(2 - 2 i)^{7}

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

arctan (f (2 x^{2} + 3))

What is expand (2x^6+(x^2)/4)^{10} ?
The solution to expand (2x^6+(x^2)/4)^{10} is