https://file.aiquickdraw.com/mathbot/file/1726810953699sp8tags4.jpg

The expression in the image is:

\[
4y^4(2xy - 2y^2)
\]

Let's simplify this step by step using the distributive property. We will multiply each term inside the parentheses by \(4y^4\).

1. First, distribute \(4y^4\) to \(2xy\):
   \[
   4y^4 \times 2xy = 8xy^5
   \]

2. Then, distribute \(4y^4\) to \(-2y^2\):
   \[
   4y^4 \times -2y^2 = -8y^6
   \]

Now, combining these, the simplified expression is:

\[
8xy^5 - 8y^6
\]

Would you like any further clarifications or details on this solution? Here are some related questions:

1. How do we apply the distributive property in algebraic expressions?
2. What are the general rules for multiplying exponents in algebra?
3. How does this problem relate to polynomial multiplication?
4. Can this expression be factored further?
5. What happens if we plug in specific values for \(x\) and \(y\)?

**Tip:** When multiplying terms with exponents, always remember to add the exponents if the bases are the same!

Simplify the expression 4y^4(2xy - 2y^2).

Learn how to simplify the algebraic expression 4y^4(2xy - 2y^2) using the distributive property and exponents. The problem involves multiplying terms with variables and powers, 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