Factorise the following - 

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

Asked by Cl_narayan | 27th Dec, 2019, 07:24: AM

Expert Answer:

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)

Answered by  | 27th Dec, 2019, 09:45: AM