What is expand (p+1/p)^5 ?

The solution to expand (p+1/p)^5 is p^5+5p^3+10p+(10)/p+5/(p^3)+1/(p^5)

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expand (p+1/p)^5

expand

(p + \frac{1}{p})^{5}

p^{5} + 5 p^{3} + 10 p + \frac{10}{p} + \frac{5}{p ^{3}} + \frac{1}{p ^{5}}

Solution steps

(p + \frac{1}{p})^{5}

Apply binomial theorem:

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

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

= i = 0 \sum 5 (i 5) p^{(5 - i)} (\frac{1}{p})^{i}

Expand summation

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

Simplify

\frac{5 !}{0 ! ( 5 - 0 ) !} p^{5} (\frac{1}{p})^{0} : p^{5}

Simplify

\frac{5 !}{1 ! ( 5 - 1 ) !} p^{4} (\frac{1}{p})^{1} : 5 p^{3}

Simplify

\frac{5 !}{2 ! ( 5 - 2 ) !} p^{3} (\frac{1}{p})^{2} : 10 p

Simplify

\frac{5 !}{3 ! ( 5 - 3 ) !} p^{2} (\frac{1}{p})^{3} : \frac{10}{p}

Simplify

\frac{5 !}{4 ! ( 5 - 4 ) !} p^{1} (\frac{1}{p})^{4} : \frac{5}{p ^{3}}

Simplify

\frac{5 !}{5 ! ( 5 - 5 ) !} p^{0} (\frac{1}{p})^{5} : \frac{1}{p ^{5}}

= p^{5} + 5 p^{3} + 10 p + \frac{10}{p} + \frac{5}{p ^{3}} + \frac{1}{p ^{5}}

\frac{( k + 1 ) ( k + 2 ) ( k + 3 ) ( k + 4 )}{4}

(2, 5) y (- 1, - 4)

\frac{d x}{( x + 2 ) ( x - 3 )}

(x - a)^{2} + (y - b)^{2}

lo g_{10} (t^{3})

What is expand (p+1/p)^5 ?
The solution to expand (p+1/p)^5 is p^5+5p^3+10p+(10)/p+5/(p^3)+1/(p^5)