3x2y+2y2 find the value of this polynomial if x = 3 and y=-2

To find the value of the polynomial \(3x^2y + 2y^2\) when \(x = 3\) and \(y = -2\), follow these steps:

1. **Substitute the values of \(x\) and \(y\)** into the polynomial:
   \[
   3(3)^2(-2) + 2(-2)^2
   \]

2. **Calculate \(x^2\) and \(y^2\)**:
   \[
   3^2 = 9 \quad \text{and} \quad (-2)^2 = 4
   \]

3. **Multiply the coefficients**:
   \[
   3 \times 9 \times (-2) = 3 \times (-18) = -54
   \]
   \[
   2 \times 4 = 8
   \]

4. **Add the results**:
   \[
   -54 + 8 = -46
   \]

So, the value of the polynomial when \(x = 3\) and \(y = -2\) is \(-46\).

Would you like more details or have any questions?

Here are 5 related questions to further your understanding:
1. How do you evaluate a polynomial with more than two variables?
2. What happens when the sign of \(x\) and \(y\) changes in the given polynomial?
3. How would you expand and simplify polynomials like this one?
4. Can you explain the process of factorization for similar polynomials?
5. What are the implications of a negative result in a polynomial evaluation?

**Tip:** Always be careful with the signs when substituting negative values into polynomials.

Learn how to evaluate the polynomial 3x^2y + 2y^2 when x = 3 and y = -2. This problem covers polynomial evaluation through substitution and coefficient multiplication, suitable for students in Grades 7-9.

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