Factorize each of the following expressions:
(1) `36l^2-(m+n)^2`
(2) `25 x^4y^4-1`
(3)`a^4-1/(b^4)`
(4) `x^3-144 x`

Explanation

using identities `(a^2-b^2)=(a-b)(a+b)`
(i)`36 l^2-(m+n)^2`
`= (6l)^2 -(m + n)^2 `
`= (6l + m + n) (6l -m-n)`

(ii) `25 x^4y^4-1`
`=(5x^2y^2)^2 - 1`
`=(5x^2y^2 + 1)(5x^2y^2-1)`

(iii)`a^4-1/(b^4)`
`=(a^2)^2-(1/b^2)^2`
`=(a^2+1/b^2)(a^2-1/b^2)`

(iv) `x^3-144 x`
`=x(x^2 - 144)`
`= x [ (x)^2 - (12)^2]`
`= (x) (x+12)(x-12)`