Question: Factor completely. 1, minus, 64, x, squared
1−64x^2
1. **State the problem:** Factor the expression $$1 - 64x^2$$ completely.
2. **Recognize the formula:** This is a difference of squares, which follows the rule:
$$a^2 - b^2 = (a - b)(a + b)$$
3. **Identify terms:** Here, $$1 = 1^2$$ and $$64x^2 = (8x)^2$$.
4. **Apply the difference of squares formula:**
$$1 - 64x^2 = 1^2 - (8x)^2 = (1 - 8x)(1 + 8x)$$
5. **Final answer:**
$$\boxed{(1 - 8x)(1 + 8x)}$$