Factorize each of the following algebraic expressions:
(i)`x^4-81 y^4`
(ii) `2x^5-2x`
(iii)`3x^4-243`
(iv) `2-50 x^2`

Explanation

Using identities `(a^2-b^2)=(a-b)(a+b)`
(i)`x^4-81 y^4`
`=(x^2)^2-(9^2)^2`
`=(x^2+9y^2)(x^2-9y^2)`
`=(x -3y) ( x + 3y) (x² +9y²)`

(ii) `2x^5-2x`
`=2x(x^4 - 1)`
`=2x[(x^2)^2 - (1)^2]`
`=2x(x^2 + 1)(x^2 - 1)`
`=2x(x^2 + 1)[(x)^2 - (1)^2]`
`=2x(x^2 + 1)(x+1)(x-1)`
(iii)`3x^4-243`
`=3(x^4-81)`
`=3((x^2)^2-(9^2)^2)`
`=3((x^2+9^2)(x^2-9^2))`
`=3(x -3) ( x + 3) (x^2 + 9)`

(iv) `2-50 x^2`
`=2(1−25x^2)`
`=2[12−(5x)^2]`
`=2(1+5x)(1−5x)`