The expression \( t^4 - 1 \) can be factorized using the difference of squares. Here's the step-by-step factorization:

1. **Identify as a difference of squares:**
   \[
   t^4 - 1 = (t^2)^2 - 1^2
   \]
   This fits the form \( a^2 - b^2 = (a - b)(a + b) \).

2. **Apply the difference of squares:**
   \[
   t^4 - 1 = (t^2 - 1)(t^2 + 1)
   \]

3. **Further factorize \( t^2 - 1 \):**
   The term \( t^2 - 1 \) is again a difference of squares:
   \[
   t^2 - 1 = (t - 1)(t + 1)
   \]

4. **Final factorization:**
   Combining all the factors together:
   \[
   t^4 - 1 = (t - 1)(t + 1)(t^2 + 1)
   \]

Thus, the complete factorization of \( t^4 - 1 \) is:
\[
t^4 - 1 = (t - 1)(t + 1)(t^2 + 1)
\]

Would you like more details on any part of this process, or do you have any questions?

### Related Questions:
1. How do you factor higher degree polynomials?
2. What is the difference of squares, and how is it applied?
3. Can the term \( t^2 + 1 \) be further factorized?
4. How would the factorization change if the expression were \( t^4 + 1 \) instead?
5. How do you identify factorable patterns in polynomials?
6. What are irreducible polynomials over the real numbers?
7. How can polynomial division be used in factorization?
8. How do you factor a sum or difference of cubes?

### Tip:
Always check if the factors you obtain can be further factorized, especially when dealing with higher-degree polynomials.

Learn how to factorize the polynomial t^4 - 1 using the difference of squares method. Step-by-step solution provided with detailed explanations. Suitable for high school students studying algebra and polynomials.

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