To solve the expression \( y^2 + 5x^2 - 3xy \) given \( x = 4 \) and \( y = 2 \), substitute the values of \( x \) and \( y \) into the expression:

\[
y^2 + 5x^2 - 3xy
\]

Substitute \( x = 4 \) and \( y = 2 \):

\[
(2)^2 + 5(4)^2 - 3(2)(4)
\]

Now, calculate each term:

1. \( y^2 = 2^2 = 4 \)
2. \( 5x^2 = 5 \times 4^2 = 5 \times 16 = 80 \)
3. \( 3xy = 3 \times 2 \times 4 = 24 \)

So, the expression becomes:

\[
4 + 80 - 24
\]

Now, simplify:

\[
4 + 80 = 84
\]
\[
84 - 24 = 60
\]

Thus, the value of the expression is \( 60 \).

Would you like more details or have any questions about this?

Here are some related questions you might find interesting:

1. What would the value be if \( x = 3 \) and \( y = 1 \) in the expression \( y^2 + 5x^2 - 3xy \)?
2. How does the expression change if the coefficients of \( x^2 \) and \( xy \) are different?
3. What is the value of \( x^2 + y^2 \) when \( x = 4 \) and \( y = 2 \)?
4. Can you solve \( 2y^2 + 4x^2 - xy \) with the same values of \( x \) and \( y \)?
5. How does changing the sign of \( y \) to negative affect the expression?
6. What would the expression look like if you factor it?
7. How would you describe the effect of increasing \( x \) and \( y \) simultaneously?
8. What happens if both \( x \) and \( y \) are negative?

**Tip:** Always follow the order of operations (PEMDAS: Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right)) when evaluating expressions.

Learn how to evaluate the expression y^2 + 5x^2 - 3xy when x = 4 and y = 2 with a step-by-step solution. This problem covers key algebraic concepts, including substitution and simplification of expressions. Suitable for students in Grades 7-9.

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