https://file.aiquickdraw.com/mathbot/file/1727652452371d9o3lktx.jpg

The given trinomial is:

\[
x^2 - 16x + 64
\]

We will factor this using the perfect squares method.

1. Check if the first and last terms are perfect squares:
   - The first term \(x^2\) is a perfect square because \((x)^2 = x^2\).
   - The last term \(64\) is also a perfect square because \((8)^2 = 64\).

2. Check if the middle term fits the pattern of \(2ab\) where \(a\) is the square root of the first term, and \(b\) is the square root of the last term:
   - \(a = x\) and \(b = 8\).
   - \(2ab = 2 \cdot x \cdot 8 = 16x\), and indeed, the middle term is \(-16x\), which matches the pattern but with a negative sign.

Thus, the trinomial can be factored as:

\[
(x - 8)^2
\]

### Final Answer:
The factored form of the trinomial \(x^2 - 16x + 64\) is:

\[
(x - 8)^2
\]

Would you like more details or have any questions?

Here are 5 related questions you might find helpful:
1. How do you recognize a perfect square trinomial?
2. Can all trinomials be factored using the perfect squares method?
3. What is the difference between factoring by grouping and factoring perfect square trinomials?
4. How does factoring help in solving quadratic equations?
5. What if the middle term was positive, how would that change the factored form?

**Tip:** Always check if the first and last terms are perfect squares before applying the perfect squares method!

What is the factored form of the trinomial x^2 - 16x + 64, using the perfect squares method?

Learn how to factor the trinomial x^2 - 16x + 64 using the perfect squares method. This step-by-step solution covers key algebraic concepts like factoring trinomials and recognizing perfect square patterns. 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