Question

Expand the following :
[ a+1/a ]3 ?
Formula: (a+b)3=a3+3a2b+3ab2+b3

Answer 1

a^3 + 1/a^3 + 3a + 1/3a

Answer 2

$(a + b)^3 = a^3 + 3a^2b + 3ab^2 + b^3$

Find (a + 1/a)³:

$(a + \dfrac{1}{a} )^3 = a^3 + 3a^2(\dfrac{1}{a}) + 3a(\dfrac{1}{a})^2 + (\dfrac{1}{a} )^3$

$(a + \dfrac{1}{a} )^3 = a^3 + \dfrac{3a^2}{a} + \dfrac{3a}{a^2} + \dfrac{1}{a^3}$

$(a + \dfrac{1}{a} )^3 = a^3 +3a + \dfrac{3}{a} + \dfrac{1}{a^3}$