Answer: Option D
[tex](9x^2+1)(3x+1)(3x-1)[/tex]
Step-by-step explanation:
We have the following expression
[tex]81x^4-1[/tex]
We can rewrite the expression in the following way:
[tex](9x^2)^2-1^2[/tex]
Remember the following property
[tex](a+b)(a-b) = a^2 -b^2[/tex]
Then in this case [tex]a=(9x^2)[/tex] and [tex]b=1[/tex]
So we have that
[tex](9x^2)^2-1^2[/tex]
[tex](9x^2+1)(9x^2-1)[/tex]
Now we can rewrite the expression [tex]9x^2[/tex] as follows
[tex](3x)^2[/tex]
So
[tex](9x^2+1)(9x^2-1) =(9x^2+1)((3x)^2-1^2)[/tex]
Then in this case [tex]a=(3x)[/tex] and [tex]b=1[/tex]
So we have that
[tex](9x^2+1)(9x^2-1) =(9x^2+1)((3x)^2-1^2)[/tex]
[tex](9x^2+1)(9x^2-1) =(9x^2+1)(3x+1)(3x-1)[/tex]
finally the factored expression is:
[tex](9x^2+1)(3x+1)(3x-1)[/tex]
