Factorize each of the following expressions:
(1)`16 x^2-25 y^2`
(2) `27 x^2-12 y^2`
(3)`144 a^2-289 b^2`
(4) `12 m^2-27`

Explanation

using identities `(a^2-b^2)=(a-b)(a+b)`
(i)`16 x^2-25 y^2`
`=(4x)^2−(5y)^2`
`=(4x−5y)(4x+5y)`

(ii) `27 x^2-12 y^2`
`= 3 [ 9x^2 - 4y^2]`
`= 3 [ (3x)^2 - (2y)^2]`
`= 3 (3x + 2y)(3x - 2y)`

(iii)`144 a^2-289 b^2`
`= (12a)^2 – (17b)^2`
`= (12a + 17b) (12a – 17b)`

(iv) `12 m^2-27`
`= 3 (4m^2 – 9)`
`= 3 [(2m)^2 – 3^2]`
`= 3 (2m + 3) (2m – 3)`