Factorize each of the following expressions:
(i)`(2a-b)^2-16 c^2`
(ii) `(x+2y)^2-4\ (2x-y)^2`
(iii)`3a^5-48 a^3`
(iv) `a^4- 16 b^4`

Explanation

(i)`(2a-b)^2-16 c^2`
`= (2a – b)^2 – (4c)^2`
`= (2a – b + 4c) (2a – b – 4c)`

(ii) `(x+2y)^2-4\ (2x-y)^2`
`= (x + 2y)^2 – [2 (2x – y)]^2`
`= [(x + 2y) + 2 (2x – y)] [x + 2y – 2 (2x – y)]`
`= (x + 4x + 2y – 2y) (x – 4x + 2y + 2y)`
`= (5x) (4y – 3x)`

(iii)`3a^5-48 a^3`
`= 3a^3 (a^2 – 16)`
`= 3a^3 (a^2 – 42)`
`= 3a^3 (a + 4) (a – 4)`
(iv) `a^4- 16 b^4`
`= (a^2)^2 – (4b^2)^2 `
`= (a^2 + 4b^2) (a^2 – 4b^2) `
`= (a^2 + 4b^2) (a + 2b) (a – 2b)`