The given expression is:

\[
w^2 - 8w + 16
\]

This is a quadratic expression, and we can attempt to factor it. Let's proceed step by step.

We are looking for two numbers that multiply to \( 16 \) (the constant term) and add up to \( -8 \) (the coefficient of \( w \)).

The numbers are \( -4 \) and \( -4 \), since:

\[
(-4) \times (-4) = 16 \quad \text{and} \quad (-4) + (-4) = -8
\]

So, the factored form of the quadratic is:

\[
(w - 4)(w - 4) \quad \text{or} \quad (w - 4)^2
\]

Thus, the expression simplifies to:

\[
(w - 4)^2
\]

Would you like a more detailed explanation of how this factoring was done? 

Here are some related questions:
1. What happens if the quadratic expression cannot be factored easily?
2. How do you solve \( (w - 4)^2 = 0 \)?
3. How does completing the square work for this expression?
4. What are the solutions to the equation \( w^2 - 8w + 16 = 0 \)?
5. How can this expression be used to find the vertex of a parabola?

**Tip**: Factoring is a useful technique for solving quadratic equations, but remember that not all quadratics can be factored easily. In such cases, using the quadratic formula might be more efficient.

Learn how to factor the quadratic equation w^2 - 8w + 16 using the factoring method. This problem covers important algebraic concepts and explains the process step by step. Suitable for students in Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation