To simplify the expression \((t + 2)(t - 11)\), you can use the distributive property (or the FOIL method for binomials):

\[
(t + 2)(t - 11) = t \cdot t + t \cdot (-11) + 2 \cdot t + 2 \cdot (-11)
\]

Now, let's simplify each term:

- \(t \cdot t = t^2\)
- \(t \cdot (-11) = -11t\)
- \(2 \cdot t = 2t\)
- \(2 \cdot (-11) = -22\)

Now, combine all the terms:

\[
t^2 - 11t + 2t - 22
\]

Combine the like terms \(-11t\) and \(2t\):

\[
t^2 - 9t - 22
\]

So, the simplified form of \((t + 2)(t - 11)\) is:

\[
t^2 - 9t - 22
\]

Would you like more details, or do you have any questions?

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Here are 8 related questions:

1. How would you expand \((t + 3)(t - 4)\)?
2. What is the result of \((t - 5)(t + 6)\)?
3. How would you simplify \((3t + 7)(t - 2)\)?
4. What happens when you expand \((t - 8)(t + 9)\)?
5. Can you factor the expression \(t^2 - 9t - 22\) back into binomials?
6. How does the FOIL method work when expanding binomials?
7. What is the expanded form of \((t + 1)(t + 12)\)?
8. How would you expand and simplify \((t + 4)(t - 10)\)?

**Tip:** When expanding binomials, carefully track the signs (positive or negative) in each term to avoid errors.

Learn how to simplify the expression (t + 2)(t - 11) with a step-by-step solution using the distributive property. This problem covers algebraic concepts such as polynomials, FOIL method, and quadratic equations. Suitable for students in Grades 7-9.

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