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To factorize \( t^2 - 8t + 16 \) in the form \( (t + a)^2 \), we can follow these steps:

### Step-by-Step Solution
1. Start with the expression:
   \[
   t^2 - 8t + 16
   \]

2. Notice that this is a quadratic trinomial, and it can be written as a perfect square. We aim to find a value \( a \) so that:
   \[
   t^2 - 8t + 16 = (t + a)^2
   \]

3. Expand \( (t + a)^2 \) to see what form it should take:
   \[
   (t + a)^2 = t^2 + 2at + a^2
   \]

4. Now, match the terms from \( t^2 - 8t + 16 \) with \( t^2 + 2at + a^2 \):
   - The coefficient of \( t \) in \( t^2 - 8t + 16 \) is \(-8\), so:
     \[
     2a = -8
     \]
     Solving for \( a \):
     \[
     a = -4
     \]

5. Substitute \( a = -4 \) and check if it satisfies the constant term:
   - When \( a = -4 \), \( a^2 = (-4)^2 = 16 \), which matches the constant term in \( t^2 - 8t + 16 \).

6. Therefore, we can rewrite \( t^2 - 8t + 16 \) as:
   \[
   t^2 - 8t + 16 = (t - 4)^2
   \]

### Conclusion
The value of \( a \) is \(-4\).

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Would you like further details on factorization techniques or any additional questions?

### Related Questions
1. How do you determine if a quadratic expression is a perfect square?
2. What is the general form of a perfect square trinomial?
3. How does completing the square help in solving quadratic equations?
4. What are other methods to factorize quadratics besides recognizing perfect squares?
5. How can you apply factorization to solve equations?

### Tip
Remember that a quadratic expression \( ax^2 + bx + c \) can often be checked for perfect squares by examining if \( b^2 = 4ac \), which is the discriminant condition for a perfect square.

t^2 - 8t + 16 can be factorised to give an expression of the form (t + a)^2, where a is an integer. Work out the value of a.

Learn how to factorise the quadratic expression t^2 - 8t + 16 into the form (t + a)^2. This problem covers key algebraic concepts, including perfect square trinomials, and is suitable for students in Grades 8-10.

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