What is expand (1-5/p)^3 ?

The solution to expand (1-5/p)^3 is (p^3-15p^2-125+75p)/(p^3)

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expand (1-5/p)^3

expand

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

\frac{p ^{3} - 15 p ^{2} - 125 + 75 p}{p ^{3}}

Solution steps

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

Apply Perfect Cube Formula:

(a - b)^{3} = a^{3} - 3 a^{2} b + 3 a b^{2} - b^{3}

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

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

Simplify

1^{3} - 3 \cdot 1^{2} \cdot \frac{5}{p} + 3 \cdot 1 \cdot (\frac{5}{p})^{2} - (\frac{5}{p})^{3} : \frac{p ^{3} - 15 p ^{2} - 125 + 75 p}{p ^{3}}

= \frac{p ^{3} - 15 p ^{2} - 125 + 75 p}{p ^{3}}

(1 + sin (x)) (cos (x))

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

- \frac{20 s}{( s ^{2} + 25 ) ^{2}}

- sec (x) (2 sin (2 x) - tan (x) cos (2 x))

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

What is expand (1-5/p)^3 ?
The solution to expand (1-5/p)^3 is (p^3-15p^2-125+75p)/(p^3)