Let's simplify the given expression:

\[
12y^2x - 36x^3y^2 + 24x^3y^2 + 48y^3x^4
\]

1. Combine like terms where possible. Start by grouping terms with common variables.

- Combine \(-36x^3y^2\) and \(24x^3y^2\):

\[
-36x^3y^2 + 24x^3y^2 = -12x^3y^2
\]

Now, substitute this into the original expression:

\[
12y^2x - 12x^3y^2 + 48y^3x^4
\]

This is the simplified form.

Would you like further details or have any questions?

Here are 5 related questions:
1. How do you factor polynomials with multiple variables?
2. What are the rules for combining like terms?
3. How can you use exponents to simplify polynomial expressions?
4. What are common factoring techniques for polynomials?
5. How do you handle negative coefficients when simplifying expressions?

**Tip:** Always check if terms share common factors before simplifying, which can reduce the expression more efficiently.

Learn how to simplify the polynomial expression 12y^2x - 36x^3y^2 + 24x^3y^2 + 48y^3x^4. This solution involves combining like terms and applying fundamental algebraic properties. Suitable for students in Grades 9-10.

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