Given the polynomial 4x2y4 − 9x2y6, rewrite as a product of polynomials.

 (2xy2 − 3xy3)(2xy2 + 3xy3) (2xy2 − 3xy3)(2xy2 − 3xy3) (4xy2 + 9xy3)(xy2 − xy3) (4xy2 − 9xy3)(xy2 − xy3)

We are given the polynomial expression \( 4x^2y^4 - 9x^2y^6 \), and the goal is to rewrite it as a product of polynomials.

### Step-by-step process:

1. **Factor out the greatest common factor (GCF):**
   - The GCF of the two terms \( 4x^2y^4 \) and \( 9x^2y^6 \) is \( x^2y^4 \), since it appears in both terms.

   \[
   4x^2y^4 - 9x^2y^6 = x^2y^4(4 - 9y^2)
   \]

2. **Factor the difference of squares:**
   - The expression \( 4 - 9y^2 \) is a difference of squares, as it can be rewritten as:

   \[
   4 - 9y^2 = (2 - 3y)(2 + 3y)
   \]

3. **Final factorization:**
   - Now, substitute this back into the equation:

   \[
   x^2y^4(4 - 9y^2) = x^2y^4(2 - 3y)(2 + 3y)
   \]

Thus, the factored form of the polynomial is:

\[
x^2y^4(2 - 3y)(2 + 3y)
\]

### Conclusion:
The correct factorization is \( x^2y^4(2 - 3y)(2 + 3y) \).

Let me know if you'd like further explanation, or have any questions!

Here are 5 related questions:
1. How do you factor trinomials?
2. What is the process for factoring a sum of cubes?
3. How do you identify the GCF of a polynomial?
4. What are the rules for factoring perfect squares?
5. How do you solve polynomials after factoring?

**Tip:** When factoring, always check for a greatest common factor (GCF) before applying other factoring techniques.

Given the polynomial 4x^2y^4 − 9x^2y^6, rewrite as a product of polynomials.

Learn how to factor the polynomial 4x^2y^4 − 9x^2y^6 into a product of polynomials. This step-by-step guide explains the process of factoring out the greatest common factor and applying the difference of squares formula, suitable for high school students in Grades 9-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation