Multiply. 2 x´-8xy+12y x+10y x-100y ² 5х-10y Simplify your answer as much as possible.

Algebra for College Students
10th Edition
ISBN:9781285195780
Author:Jerome E. Kaufmann, Karen L. Schwitters
Publisher:Jerome E. Kaufmann, Karen L. Schwitters
Chapter9: Polynomial And Rational Functions
Section9.3: Polynomial Equations
Problem 5CQ
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### Rational Expressions
#### Multiplying Rational Expressions Involving Multivariate Quadratics

**Problem:**

Multiply.

\[
\frac{x^2 - 8xy + 12y^2}{x^2 - 100y^2} \cdot \frac{x + 10y}{5x - 10y}
\]

**Instructions:**

Simplify your answer as much as possible.

---

**Diagram Explanation:**

Below the problem statement, there's a rectangular input box where learners can enter their answer. Next to the input box, there are three buttons:

1. A button with two squares and a line between them, suggesting it may open a tool or palette for entering fractions or expressions.
2. A circular arrow, commonly used as an undo button.
3. A question mark, likely to provide help or hints.

These tools are meant to assist in constructing and simplifying rational expressions.

---

For educators:

- Emphasize the importance of factoring both the numerators and denominators before simplifying the expression.
- Ensure students understand how to cancel out common factors to simplify the resulting rational expression.

---

This problem helps students practice multiplying and simplifying multivariate quadratic rational expressions, reinforcing their understanding of algebraic manipulation and factorization.
Transcribed Image Text:### Rational Expressions #### Multiplying Rational Expressions Involving Multivariate Quadratics **Problem:** Multiply. \[ \frac{x^2 - 8xy + 12y^2}{x^2 - 100y^2} \cdot \frac{x + 10y}{5x - 10y} \] **Instructions:** Simplify your answer as much as possible. --- **Diagram Explanation:** Below the problem statement, there's a rectangular input box where learners can enter their answer. Next to the input box, there are three buttons: 1. A button with two squares and a line between them, suggesting it may open a tool or palette for entering fractions or expressions. 2. A circular arrow, commonly used as an undo button. 3. A question mark, likely to provide help or hints. These tools are meant to assist in constructing and simplifying rational expressions. --- For educators: - Emphasize the importance of factoring both the numerators and denominators before simplifying the expression. - Ensure students understand how to cancel out common factors to simplify the resulting rational expression. --- This problem helps students practice multiplying and simplifying multivariate quadratic rational expressions, reinforcing their understanding of algebraic manipulation and factorization.
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