Given:
The expression is
[tex]81x^4-1[/tex]
To find:
The factorized form of given expression.
Solution:
We have,
[tex]81x^4-1[/tex]
It can be rewritten as
[tex]=3^4x^4-1^2[/tex]
[tex]=(3x)^4-1^2[/tex] [tex][\because a^xb^x=(ab)^x][/tex]
[tex]=((3x)^2-1)((3x)^2+1)[/tex] [tex][\because a^2-b^2=(a-b)(a+b)][/tex]
[tex]=(3x+1)(3x-1)(3x+1)(3x-1)[/tex] [tex][\because a^2-b^2=(a-b)(a+b)][/tex]
This is the complete factorized form. It can also written as
[tex]=(3x+1)^2(3x-1)^2[/tex]
Therefore, the complete factorized form is [tex](3x+1)(3x-1)(3x+1)(3x-1)[/tex].
