Question

Expand the following:

`((2a)/(5b) - (5b)/(2a))^2`

Answer 1

`((2a)/(5b) - (5b)/(2a))^2`

Let, `x = (2a)/(5b), y = (5b)/(2a)`

Thus, 

`((2a)/(5b) - (5b)/(2a))^2 = ((2a)/(5b))^2 - 2((2a)/(5b) xx (5b)/(2a)) + ((5b)/(2a))^2`  ...[Using (x − y)² = x² − 2xy + y²]

`((2a)/(5b) - (5b)/(2a))^2 = (4a^2)/(25b^2) - 2 xx (2a)/(5b) xx (5b)/(2a) + (25b^2)/(4a^2)`

∴ `((2a)/(5b) - (5b)/(2a))^2 = (4a^2)/(25b^2) - 2 + (25b^2)/(4a^2)`