1. **State the problem:** Fully factorize the expression $1 - 81y^4$. 2. **Recognize the form:** This is a difference of squares since $1 = 1^2$ and $81y^4 = (9y^2)^2$. 3. **Apply difference of squares formula:** $$a^2 - b^2 = (a - b)(a + b)$$ Here, $a = 1$ and $b = 9y^2$. 4. **Factor the expression:** $$1 - 81y^4 = (1 - 9y^2)(1 + 9y^2)$$ 5. **Check if further factorization is possible:** The term $1 - 9y^2$ is again a difference of squares: $$1 - 9y^2 = (1)^2 - (3y)^2 = (1 - 3y)(1 + 3y)$$ 6. **Final fully factored form:** $$1 - 81y^4 = (1 - 3y)(1 + 3y)(1 + 9y^2)$$ This is the complete factorization since $1 + 9y^2$ cannot be factored further over the real numbers.