Let's simplify the expression step by step:

\[
t^2 - 2t + (1)^2 - (1)^2 + 3
\]

1. Simplify the terms \((1)^2\) and \(-(1)^2\):

\[
t^2 - 2t + 1 - 1 + 3
\]

2. Notice that \(+1\) and \(-1\) cancel each other out:

\[
t^2 - 2t + 3
\]

So, the simplified expression is:

\[
t^2 - 2t + 3
\]

Let me know if you'd like further details or have any questions!

Here are 5 related questions to explore further:
1. How can we solve quadratic equations like \(t^2 - 2t + 3 = 0\)?
2. What are the roots of the equation \(t^2 - 2t + 3\) using the quadratic formula?
3. Can this expression be factored, or is it prime?
4. How does the discriminant help in analyzing quadratic equations?
5. What is the graph of \(t^2 - 2t + 3\) and its key features?

**Tip:** In quadratic expressions, the discriminant \(\Delta = b^2 - 4ac\) helps determine the nature of the roots (real or complex).

Explore how to simplify the quadratic expression t² - 2t + (1)² - (1)² + 3 through a step-by-step breakdown. This algebraic problem is ideal for students learning to manipulate and simplify quadratic expressions. Suitable for Grades 7-9.

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