Answer:
Step-by-step explanation:
First, we notice that (81) is a perfect square, as it can be expressed as (9^2).
Similarly, (x^8) is also a perfect square, since it can be written as ((x4)2).
Now, let’s use the difference of squares formula to factor the expression:
[ a^2 - b^2 = (a + b)(a - b) ]
Where:
(a = x^4)
(b = 9)
Applying the formula:
[ 81 - x^8 = (9 + x^4)(9 - x^4) ]
Further simplifying:
[ 81 - x^8 = (3 + x^2)(3 - x^2)(9 + x^4) ]
Therefore, the fully factored form of (81 - x^8) is ((3 + x^2)(3 - x^2)(9 + x^4)).
