4x 
4
 +20x 
2
 y+25y 
2
 

Which of the following is equivalent to the given expression?

Let's analyze the expression:

\[
4x^4 + 20x^2y + 25y^2
\]

This looks like a quadratic expression that can potentially be factored. We can attempt factoring it as a perfect square trinomial.

### Step-by-step Factorization:

1. **First term:** \( 4x^4 \) is a perfect square, since:
   \[
   4x^4 = (2x^2)^2
   \]

2. **Last term:** \( 25y^2 \) is also a perfect square:
   \[
   25y^2 = (5y)^2
   \]

3. **Middle term:** \( 20x^2y \) can be written as \( 2 \times (2x^2) \times (5y) \), which matches the middle term for a perfect square trinomial.

Thus, the expression can be factored as:
\[
(2x^2 + 5y)^2
\]

### Final Answer:
The expression \( 4x^4 + 20x^2y + 25y^2 \) is equivalent to:

\[
(2x^2 + 5y)^2
\]

Would you like any further explanation or details?

Here are 5 related questions:
1. How do you recognize a perfect square trinomial?
2. What are the steps to factor a quadratic expression?
3. Can all quadratic expressions be factored into perfect squares?
4. What is the geometric interpretation of factoring?
5. How can factoring help in solving equations?

**Tip:** Always check if the middle term fits the form \( 2ab \) when looking for perfect square trinomials.

Which of the following is equivalent to the given expression: 4x^4 + 20x^2y + 25y^2?

Explore the step-by-step factorization of the algebraic expression 4x^4 + 20x^2y + 25y^2, identified as a perfect square trinomial. Learn key algebra concepts, including factoring techniques, and understand how to recognize and solve these expressions. Suitable for high school students in Grades 9-12.

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