To factor the quadratic expression \( t^2 + 8t + 16 \), follow these steps:

1. Recognize the form: This is a trinomial in the form \( t^2 + bt + c \).
2. Find two numbers that multiply to give 16 (the constant term) and add to give 8 (the coefficient of \( t \)).

The numbers that satisfy this are 4 and 4 because:

- \( 4 \times 4 = 16 \)
- \( 4 + 4 = 8 \)

3. Therefore, the factored form of the expression is:

\[
(t + 4)(t + 4) = (t + 4)^2
\]

Thus, \( t^2 + 8t + 16 = (t + 4)^2 \).

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

Here are 5 related questions to explore further:
1. How would you factor \( t^2 - 8t + 16 \)?
2. Can you factor \( t^2 + 8t + 15 \)?
3. What is the factored form of \( t^2 + 10t + 25 \)?
4. How do you solve \( t^2 + 8t + 16 = 0 \)?
5. What are the roots of \( t^2 + 6t + 9 \)?

**Tip**: Always check if a quadratic is a perfect square trinomial when factoring; it simplifies the process!

Learn how to factor the quadratic expression t² + 8t + 16 with this detailed step-by-step solution. This guide explains how to identify and factor a perfect square trinomial, making it ideal for students in Grades 8-10 looking to master algebraic techniques.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation