The expression \( x^2 - 24xy + 144y^2 \) is a perfect square trinomial. Here's the factoring process:

1. The first term is \( x^2 \), which is the square of \( x \).
2. The last term is \( 144y^2 \), which is the square of \( 12y \) (since \( 12y \times 12y = 144y^2 \)).
3. The middle term, \( -24xy \), is twice the product of \( x \) and \( 12y \) (since \( 2 \times x \times 12y = 24xy \)).

Thus, the expression can be factored as:
\[
x^2 - 24xy + 144y^2 = (x - 12y)^2
\]

Would you like a detailed explanation of any step?

Here are 5 related questions to explore further:
1. How do you recognize a perfect square trinomial?
2. Can all quadratic expressions be factored like this one?
3. What is the difference between factoring and solving a quadratic equation?
4. How would you factor a quadratic if it's not a perfect square trinomial?
5. What is the geometric interpretation of a perfect square trinomial?

**Tip:** When factoring, always check if the quadratic fits the form of a perfect square trinomial before using more complex methods.

Learn how to factor the perfect square trinomial x^2 - 24xy + 144y^2 with a step-by-step solution. This problem covers key algebra concepts, including recognizing and factoring perfect square trinomials. 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