Factorize:
(i)`9a^2-16 b^2`
(ii) `36 a^2-(x-y)^2`
(iii)`80 a^2-45 b^2`
(iv) `(3a-b)^2-9c^2`

Explanation

using identities `(a^2-b^2)=(a-b)(a+b)`
(i)`9a^2-16 b^2`
`= ( 3a )^2 - ( 4 b )^2`
`= ( 3a + 4b ) ( 3a - 4b )`

(ii) `36 a^2-(x-y)^2`
`= ( 36a )^2 - ( x-y)^2`
`=(6a+x-y)(6a-x+y)`

(iii)`80 a^2-45 b^2`
`=5(16a^2−9b^2)`
`=5[(4a)^2−(3b)^2]`
`=5(4a+3b)(4a−3b)`
(iv)`(3a-b)^2-9c^2`
`= (3a-b)^2 - (3c)^2`
`=(3a-b+3c)(3a-b-3c)`