Question

81x^4-1 factor with steps

Answer 1

Given:

The expression is

`81x^4-1`

To find:

The factorized form of given expression.

Solution:

We have,

`81x^4-1`

It can be rewritten as

`=3^4x^4-1^2`

`=(3x)^4-1^2`
`[\because a^xb^x=(ab)^x]`

`=((3x)^2-1)((3x)^2+1)`
`[\because a^2-b^2=(a-b)(a+b)]`

`=(3x+1)(3x-1)(3x+1)(3x-1)`
`[\because a^2-b^2=(a-b)(a+b)]`

This is the complete factorized form. It can also written as

`=(3x+1)^2(3x-1)^2`

Therefore, the complete factorized form is
`(3x+1)(3x-1)(3x+1)(3x-1)`.