https://file.aiquickdraw.com/mathbot/file/1727036376965e1tkevzk.jpg

To solve the expression in question 24, we need to divide the polynomial by \( 2xy \). The expression is:

\[
\frac{10x^2 y^3 - 8xy^3 + 4xy}{2xy}
\]

We will divide each term in the numerator by \( 2xy \) individually:

1. \( \frac{10x^2 y^3}{2xy} = \frac{10}{2} \cdot \frac{x^2}{x} \cdot \frac{y^3}{y} = 5xy^2 \)
2. \( \frac{-8xy^3}{2xy} = \frac{-8}{2} \cdot \frac{xy^3}{xy} = -4y^2 \)
3. \( \frac{4xy}{2xy} = \frac{4}{2} \cdot \frac{xy}{xy} = 2 \)

Now, putting it all together:

\[
5xy^2 - 4y^2 + 2
\]

The correct option is the first one: \( 5xy^2 - 4y^2 + 2 \).

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

Here are 5 related questions for practice:

1. How do you divide a polynomial by a monomial in general?
2. What happens when one of the terms has a zero coefficient after division?
3. How can we check the result of a polynomial division?
4. What other operations can you perform between polynomials (e.g., addition, subtraction)?
5. What are the properties of exponents used in simplifying terms?

**Tip:** Always simplify each term separately when dividing by a monomial.

Divide: \( \frac{10x^2y^3 - 8xy^3 + 4xy}{2xy} \)

Learn how to divide the polynomial expression 10x^2y^3 - 8xy^3 + 4xy by 2xy. This step-by-step solution simplifies each term individually, applying the law of exponents and basic algebraic operations. Suitable for 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