https://file.aiquickdraw.com/mathbot/file/172551164542790o3ri7m.jpg

The equation in the image is:

\[
y^2 = (xy - x^2)(y).
\]

Let's solve this equation step by step.

### Step 1: Expand and simplify the equation

First, let's expand the right-hand side:

\[
y^2 = xy \cdot y - x^2 \cdot y.
\]

This simplifies to:

\[
y^2 = xy^2 - x^2y.
\]

### Step 2: Rearrange the equation

Now, bring all terms to one side:

\[
y^2 - xy^2 + x^2y = 0.
\]

### Step 3: Factor the equation

Factor out the common terms:

\[
y(y - xy + x^2) = 0.
\]

### Step 4: Solve for \(y\)

This equation has two solutions:

1. \(y = 0\)
2. \(y - xy + x^2 = 0 \implies y(1 - x) = x^2 \implies y = \frac{x^2}{1 - x}\), provided \(x \neq 1\).

### Final Solutions

The solutions for \(y\) are:

1. \(y = 0\)
2. \(y = \frac{x^2}{1 - x}\) (when \(x \neq 1\)).

Would you like more details, or do you have any questions?

### Related Questions:

1. What happens when \(x = 1\) in the equation?
2. Can you find any points where both solutions for \(y\) intersect?
3. How would the graph of this equation look like?
4. What are the asymptotes of the function \(y = \frac{x^2}{1 - x}\)?
5. How does changing \(x\) affect the value of \(y\)?

**Tip:** When solving equations, always look for common factors to simplify the expression.

This solution explores the factoring of the equation y^2 = (xy - x^2)y. Key concepts include expanding, simplifying, and solving quadratic equations. Suitable for students in Grades 9-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation