factor completely
81x^4 - 81
possible choices are::
(9x^2 + 9)(9x^2 - 9)
OR
(9x^2 +9)(3x + 3)(3x - 3)
No reason to stop there. Factor out all those 3's:
81(x^2+1)(x-1)(x+1)
If you must pick one of those choices, then use the last one, since it factors the 9x^2-9 as well. (factor completely!)
0968763228
To factor the expression 81x^4 - 81 completely, we can start by factoring out the greatest common factor, which in this case is 9.
Step 1: Factor out the greatest common factor of 9:
9(x^4 - 1)
Now we can focus on the expression inside the parentheses, x^4 - 1. This is a difference of squares, which means it can be factored as the product of two binomials: (a^2 - b^2) = (a + b)(a - b).
Step 2: Apply the difference of squares formula:
9((x^2)^2 - 1^2)
(x^2)^2 can be simplified as x^4, and 1^2 is just 1. So we have:
9(x^4 - 1)
Step 3: Factor x^4 - 1 using the difference of squares:
9((x^2 + 1)(x^2 - 1))
The expression x^2 - 1 is also a difference of squares, which can be factored as:
9((x^2 + 1)(x + 1)(x - 1))
So the completely factored form of 81x^4 - 81 is:
9(x^2 + 1)(x + 1)(x - 1)
Therefore, the correct choice is:
(9x^2 + 9)(3x + 3)(3x - 3)