Factorize each of the following expressions:
(1)`(2x+1)^2-9x^4`
(2) `x^4-(2y-3z)^2`
(3)`a^2-b^2+a-b`
(4) `16 a^4-b^4`

Explanation

(i)`(2x+1)^2-9x^4`
`= (2x)^2 + 2(2x)(1) + (1)^2 - 9x^4`
`= 4x^2 + 4x + 1 - 9x^4`

(ii) `x^4-(2y-3z)^2`
`=(x^2)^2 - (2y-3z)^2`
`={x^2-(2y-3z)} {x^2 +(2y-3z)}`
`=(x^2-2y+3z)(x^2+2y-3z)`

(iii)`a^2-b^2+a-b`
`=(a^2 −b^2)−(a+b)`
`=(a+b)[(a−b)−1]`
`=(a+b)(a−b−1)`

(iv) `16 a^4-b^4`
`=(4a^2+b^2)(4a^2-b^2)`
`=(4a^2+b^2)(2a+b)(2a-b)`