The given expression is:

\[
6x^2 + 4xy + 3x^2y + 2y^2
\]

You can simplify this by grouping like terms. First, let's arrange the terms in a clearer format:

\[
(6x^2 + 3x^2y) + 4xy + 2y^2
\]

We can factor out common terms where possible:

1. From the first group, \(6x^2 + 3x^2y\), we can factor out \(3x^2\):
\[
3x^2(2 + y)
\]

2. The rest of the expression, \(4xy + 2y^2\), can be factored as \(2y(2x + y)\).

Thus, the simplified form becomes:

\[
3x^2(2 + y) + 2y(2x + y)
\]

Would you like more details or have any questions?

Here are 5 related questions to extend your understanding:
1. How do you factor quadratic expressions with multiple variables?
2. What is the significance of factoring in simplifying polynomials?
3. Can you solve \(6x^2 + 4xy + 3x^2y + 2y^2 = 0\) for specific values of \(x\) and \(y\)?
4. How do you apply the distributive property to polynomials like this?
5. How would you solve a quadratic equation involving terms with \(x^2\) and \(y^2\)?

**Tip:** Always check if you can factor expressions by grouping terms with common factors first.

Learn how to factor the polynomial 6x² + 4xy + 3x²y + 2y² by grouping terms and applying the distributive property. This problem explores key algebraic concepts like polynomial expressions and factoring techniques, suitable for students in Grades 9-11.

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