Factorise the following - 

1) 4m^2 +9n^2-12mn-1

Whenever you see such Questions, think of what all square can the terms be converted to.

For example in the expression 4m² +9n²-12mn-1, could you notice that 4m² can be written as (2m)² and 9n² as (3n)² . Moreover, 2 times 2m times 3n gives 12mn.

Can you now recall the identity to be used here?

(2m)² + (3n)² - 12mn -1

 

(2m)² + (3n)² - 12mn can be written as (2m - 3n)² and the overall expression becomes,

(2m - 3n)² - 1, which can be expressed as

(2m - 3n)² - (1)²

 

Use the form (a² - b²) = (a+b)(a-b)

 

This finally becomes,

(2m-3n+1)(2m-3n-1)