https://file.aiquickdraw.com/mathbot/file/1729080926490acm8mtxb.jpg

The problem in the image is:

\[
x^3 y^3 \times \left( \frac{-3}{2}(x - y) \right)
\]

Let's simplify this expression step by step.

### Step 1: Distribute \( \frac{-3}{2} \)
We distribute \( \frac{-3}{2} \) to the expression \( (x - y) \):
\[
\frac{-3}{2}(x - y) = \frac{-3}{2}x + \frac{3}{2}y
\]

### Step 2: Multiply by \( x^3 y^3 \)
Now we multiply the whole expression by \( x^3 y^3 \):
\[
x^3 y^3 \times \left( \frac{-3}{2}x + \frac{3}{2}y \right)
\]

Distribute \( x^3 y^3 \) over each term:

\[
x^3 y^3 \times \frac{-3}{2}x = \frac{-3}{2} x^{4} y^3
\]

\[
x^3 y^3 \times \frac{3}{2}y = \frac{3}{2} x^3 y^4
\]

### Final Expression:
The simplified result is:

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

Would you like more details or have any questions? Here are 5 related questions for further exploration:

1. What happens if you factor out common terms from the expression?
2. How would this expression change if additional powers were involved in \(x\) or \(y\)?
3. How do you apply the distributive property when working with fractions and variables?
4. Can you simplify this expression further by grouping terms?
5. How does multiplying polynomials affect their degrees?

**Tip:** Always check for common factors in expressions before expanding or simplifying to make the process easier!

Simplify the expression: x^3 y^3 × (-3/2)(x - y)

Learn how to simplify the algebraic expression x^3 y^3 × (-3/2)(x - y) using the distributive property. This problem covers core algebraic concepts such as polynomial multiplication and the distributive property. Ideal for students in Grades 8-10.

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