The given expression is \( 4b^2 - 30a^2b + 25a^4 \).

This expression can be factored by recognizing it as a quadratic form in terms of \( b \). Here's how you can factor it:

1. Recognize that the expression can be written as:
   \[
   4b^2 - 30a^2b + 25a^4 = (2b)^2 - 2(2b)(5a^2) + (5a^2)^2
   \]
   
2. Notice that this is a perfect square trinomial:
   \[
   (2b - 5a^2)^2
   \]
   
So, the factored form of the expression is:

\[
(2b - 5a^2)^2
\]

This is the simplified, factored version of the original expression.

Would you like more details on the steps or have any questions?

Here are five related questions to consider:

1. How do you identify a perfect square trinomial?
2. What other types of polynomial factorizations exist?
3. How can you factor trinomials that are not perfect squares?
4. What role does the discriminant play in factoring quadratic equations?
5. How do you factor polynomials with multiple variables?

**Tip:** When factoring expressions, always check if they can be rewritten as a perfect square trinomial or another special factorable form.

Learn how to factor the expression 4b² - 30a²b + 25a⁴ with a detailed step-by-step solution. Understand the concept of perfect square trinomials and how to apply it to factoring quadratic expressions. Suitable for high school students studying algebra.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation