Factorize each of the following expressions:
(1)`256 x^5-81 x`
(2) `a^4-(2b+c)^4`
(3)`(3x+4y)^4-x^4`
(4) `p^2q^2-p^4q^4`

Explanation

Using identity:`(a^2-b^2)=(a-b)(a+b)`
(i)`256 x^5-81x`
`=x(256x^4-81)`
`=x((16x)^2-(9)^2)`
`=x(16x+9)(16x-9)`

(ii) `a^4-(2b+c)^4`
`= (a^2)2 – [(2b + c)^2]^2`
`= [a^2 + (2b + c)^2] [a^2 – (2b + c)^2] `
`= [a^2 + (2b + c)^2] [a + 2b + c] [a – 2b – c]`

(iii)`(3x+4y)^4-x^4`
`=[(3x + 4y)^2]^2 – (x^2)^2`
`=[(3x−4y)^2 −x^2 ][(3x−4y)^2 +x^2 ]`
`=[(3x−4y)+x][3x−4y−x][(3x−4y)^2 +x^2 ]`
`=(4x−4y)(2x−4y)[(3x−4y)^2 +x^2 ]`
`=8(x−y)(x−2y)[9x^2 +16y^2 −24xy+x^2 ]`
`=16(x−y)(x−2y)[5x^2 +8y^2−12xy]`

(iv) `p^2q^2-p^4q^4`
`=p^2q^2(1-p^2q^2)`
`=p^2q^2(1+pq)(1-pq)`