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The given equation is \( 4x^2 + xy \), where \( x = 3 \) and \( y = -2 \). Let's substitute these values into the equation and calculate the result.

\[
4x^2 + xy = 4(3)^2 + (3)(-2)
\]

Now, simplifying step-by-step:

\[
4(3)^2 = 4(9) = 36
\]
\[
3(-2) = -6
\]
\[
36 + (-6) = 30
\]

Thus, the value of \( 4x^2 + xy \) is \( 30 \). The correct option is **30**.

Would you like more details or have any questions? 

Here are five related questions for practice:
1. What is the value of \( 4x^2 + xy \) if \( x = 4 \) and \( y = 2 \)?
2. How do you simplify expressions with variables when given specific values?
3. If \( y = 0 \), what will the equation \( 4x^2 + xy \) simplify to?
4. What is the importance of the order of operations in solving expressions?
5. How do negative values affect the terms in polynomial expressions?

**Tip:** Always substitute carefully and follow the correct order of operations (PEMDAS: Parentheses, Exponents, Multiplication/Division, Addition/Subtraction).

Work out the value of 4x^2 + xy, when x = 3 and y = -2.

Learn how to solve the algebraic expression 4x^2 + xy by substituting x = 3 and y = -2. This problem involves key algebraic concepts such as substitution and polynomial expressions. Suitable for students in Grades 7-9.

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