Option D
![(9x^2+1)(3x+1)(3x-1)](/tpl/images/0055/9363/3fc81.png)
Step-by-step explanation:
We have the following expression
![81x^4-1](/tpl/images/0055/9363/87132.png)
We can rewrite the expression in the following way:
![(9x^2)^2-1^2](/tpl/images/0055/9363/ed7b8.png)
Remember the following property
![(a+b)(a-b) = a^2 -b^2](/tpl/images/0055/9363/01697.png)
Then in this case
and ![b=1](/tpl/images/0055/9363/a9f88.png)
So we have that
![(9x^2)^2-1^2](/tpl/images/0055/9363/ed7b8.png)
![(9x^2+1)(9x^2-1)](/tpl/images/0055/9363/914a9.png)
Now we can rewrite the expression Β
as follows
![(3x)^2](/tpl/images/0055/9363/915e4.png)
So
![(9x^2+1)(9x^2-1) =(9x^2+1)((3x)^2-1^2)](/tpl/images/0055/9363/f02d6.png)
Then in this case
and ![b=1](/tpl/images/0055/9363/a9f88.png)
So we have that
![(9x^2+1)(9x^2-1) =(9x^2+1)((3x)^2-1^2)](/tpl/images/0055/9363/f02d6.png)
![(9x^2+1)(9x^2-1) =(9x^2+1)(3x+1)(3x-1)](/tpl/images/0055/9363/e5ded.png)
finally the factored expression is:
![(9x^2+1)(3x+1)(3x-1)](/tpl/images/0055/9363/3fc81.png)