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.