https://file.aiquickdraw.com/mathbot/file/1726065120466i2e1kx0a.jpg

The expression provided in the image is:

\[
x^2y^3 - 2y^3 - 2x^2 + 4
\]

Let's factor this expression step by step.

### Step 1: Group the terms.
We can group the terms in pairs:
\[
(x^2y^3 - 2y^3) - (2x^2 - 4)
\]

### Step 2: Factor common terms from each group.
For the first group, \( x^2y^3 - 2y^3 \), we can factor out \( y^3 \):
\[
y^3(x^2 - 2)
\]

For the second group, \( -2x^2 + 4 \), we can factor out \( -2 \):
\[
-2(x^2 - 2)
\]

Now, the expression becomes:
\[
y^3(x^2 - 2) - 2(x^2 - 2)
\]

### Step 3: Factor out the common binomial factor \( (x^2 - 2) \).
We have the common factor \( (x^2 - 2) \) in both terms, so we can factor it out:
\[
(x^2 - 2)(y^3 - 2)
\]

Thus, the factored form of the expression \( x^2y^3 - 2y^3 - 2x^2 + 4 \) is:
\[
(x^2 - 2)(y^3 - 2)
\]

### Answer:
The correct option is:
\[
(x^2 - 2)(y^3 - 2)
\]

Do you want more details, or have any questions?

Here are 5 related questions for practice:
1. How do you factor a common binomial from two terms?
2. How would you factor the expression \( x^3y^2 - 3y^2 - 3x^3 + 9 \)?
3. What method can be used to factor trinomials?
4. Can you factor \( x^4 - 16 \)?
5. How would you factor \( 3xy - 6x + 9y - 18 \)?

**Tip**: Always check for a common factor before trying more complex factoring techniques.

What is the factored form of x^2y^3 - 2y^3 - 2x^2 + 4?

Learn how to factor the polynomial expression x^2y^3 - 2y^3 - 2x^2 + 4. This step-by-step guide covers key algebraic techniques, including factoring by grouping and recognizing common binomial factors. Ideal for high school students in Grades 9-12.

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