https://file.aiquickdraw.com/mathbot/file/1725564323797euh7hs4w.jpg

To solve the problem, we need to distribute the term \(-8ab\) to each term inside the parentheses. Here’s how it is done:

Given:

\[
-8ab(xa^2 + ya^5 - 4)
\]

We distribute \(-8ab\) to each term inside the parentheses:

1. Distribute to the first term:  
   \[
   -8ab \cdot xa^2 = -8ab \cdot xa^2 = -8a^3bx
   \]

2. Distribute to the second term:  
   \[
   -8ab \cdot ya^5 = -8a^5by
   \]

3. Distribute to the third term:  
   \[
   -8ab \cdot (-4) = 32ab
   \]

Putting it all together:

\[
-8a^3bx - 8a^5by + 32ab
\]

Thus, the answer is:

\[
-8a^3bx - 8a^5by + 32ab
\]

If you have any questions or want more details, feel free to ask!

### Follow-Up Questions:
1. How do you handle polynomial distribution problems like this one?
2. What is the distributive property, and how does it work in algebra?
3. Can you provide another example of distributing a monomial across a trinomial?
4. How would the answer change if the expression inside the parentheses had different signs?
5. How do you simplify expressions with negative coefficients?

**Tip:** Remember that the distributive property works both ways—multiplying out as well as factoring in.

This problem involves distributing a monomial (-8ab) across a trinomial (xa^2 + ya^5 - 4) using the distributive property. Detailed step-by-step solution is provided, 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