What is expand (1-5/p)^4 ?

The solution to expand (1-5/p)^4 is 1-(20)/p+(150)/(p^2)-(500)/(p^3)+(625)/(p^4)

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expand (1-5/p)^4

expand

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

1 - \frac{20}{p} + \frac{150}{p ^{2}} - \frac{500}{p ^{3}} + \frac{625}{p ^{4}}

Solution steps

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

Apply binomial theorem:

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

a = 1, b = - \frac{5}{p}

= i = 0 \sum 4 (i 4) \cdot 1^{(4 - i)} (- \frac{5}{p})^{i}

Expand summation

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

Simplify

\frac{4 !}{0 ! ( 4 - 0 ) !} \cdot 1^{4} (- \frac{5}{p})^{0} : 1

Simplify

\frac{4 !}{1 ! ( 4 - 1 ) !} \cdot 1^{3} (- \frac{5}{p})^{1} : - \frac{20}{p}

Simplify

\frac{4 !}{2 ! ( 4 - 2 ) !} \cdot 1^{2} (- \frac{5}{p})^{2} : \frac{150}{p ^{2}}

Simplify

\frac{4 !}{3 ! ( 4 - 3 ) !} \cdot 1^{1} (- \frac{5}{p})^{3} : - \frac{500}{p ^{3}}

Simplify

\frac{4 !}{4 ! ( 4 - 4 ) !} \cdot 1^{0} (- \frac{5}{p})^{4} : \frac{625}{p ^{4}}

= 1 - \frac{20}{p} + \frac{150}{p ^{2}} - \frac{500}{p ^{3}} + \frac{625}{p ^{4}}

\frac{- 5 x - 20}{( x - 3 ) ^{2}}

- 32 e^{2 t} U (t - 9)

(x + 2 x y - y sin (2 x)) d y

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

2 y (x + 1) d y

What is expand (1-5/p)^4 ?
The solution to expand (1-5/p)^4 is 1-(20)/p+(150)/(p^2)-(500)/(p^3)+(625)/(p^4)