What is expand (m+1/m)^6 ?

The solution to expand (m+1/m)^6 is m^6+6m^4+15m^2+20+(15)/(m^2)+6/(m^4)+1/(m^6)

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expand (m+1/m)^6

expand

(m + \frac{1}{m})^{6}

m^{6} + 6 m^{4} + 15 m^{2} + 20 + \frac{15}{m ^{2}} + \frac{6}{m ^{4}} + \frac{1}{m ^{6}}

Solution steps

(m + \frac{1}{m})^{6}

Apply binomial theorem:

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

a = m, b = \frac{1}{m}

= i = 0 \sum 6 (i 6) m^{(6 - i)} (\frac{1}{m})^{i}

Expand summation

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

Simplify

\frac{6 !}{0 ! ( 6 - 0 ) !} m^{6} (\frac{1}{m})^{0} : m^{6}

Simplify

\frac{6 !}{1 ! ( 6 - 1 ) !} m^{5} (\frac{1}{m})^{1} : 6 m^{4}

Simplify

\frac{6 !}{2 ! ( 6 - 2 ) !} m^{4} (\frac{1}{m})^{2} : 15 m^{2}

Simplify

\frac{6 !}{3 ! ( 6 - 3 ) !} m^{3} (\frac{1}{m})^{3} : 20

Simplify

\frac{6 !}{4 ! ( 6 - 4 ) !} m^{2} (\frac{1}{m})^{4} : \frac{15}{m ^{2}}

Simplify

\frac{6 !}{5 ! ( 6 - 5 ) !} m^{1} (\frac{1}{m})^{5} : \frac{6}{m ^{4}}

Simplify

\frac{6 !}{6 ! ( 6 - 6 ) !} m^{0} (\frac{1}{m})^{6} : \frac{1}{m ^{6}}

= m^{6} + 6 m^{4} + 15 m^{2} + 20 + \frac{15}{m ^{2}} + \frac{6}{m ^{4}} + \frac{1}{m ^{6}}

(\times + 1)^{2}

6 x \times 6 x

b x + x

3 + 48

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

What is expand (m+1/m)^6 ?
The solution to expand (m+1/m)^6 is m^6+6m^4+15m^2+20+(15)/(m^2)+6/(m^4)+1/(m^6)