Question

Expand.

`((5x)/y + y/(5x))^3`

Answer 1

`((5x)/y + y/(5x))^3`

(a + b)³ = a³ + 3a²b + 3ab² + b³

= `((5x)/y)^3 + 3 xx ((5x)/y)^2 xx (y/(5x)) + 3 xx ((5x)/y) xx (y/(5x))^2 + (y/(5x))^3`

= `(125x^3)/(y^3) + 3 xx (25x^2)/(y^2) xx y/(5x) + 3 xx (5x)/y xx (y^2)/(25x^2) + y^3/(125x^3)`

= `(125x^3)/(y^3) + (3 xx 25x)/y xx 1/5 + 3 xx 5 xx y/(25x) + (y^3)/(125x^3)`

= `(125x^3)/(y^3) + (15x)/y + (3y)/(5x) + (y^3)/(125x^3)`

∴ `((5x)/y + y/(5x))^3 = (125x^3)/(y^3) + (15x)/y + (3y)/(5x) + (y^3)/(125x^3)`