Let's solve the given expressions with the values $x = 3$ and $y = 5$.

Part (a): $4x - 2y$

Substitute $x = 3$ and $y = 5$ into the expression:

$4x - 2y = 4(3) - 2(5)$

Now, calculate:

$4(3) = 12$ $2(5) = 10$ $12 - 10 = 2$

So, the value of $4x - 2y$ is $2$.

Part (b): $2x^2 + 3y^2$

Substitute $x = 3$ and $y = 5$ into the expression:

$2x^2 + 3y^2 = 2(3^2) + 3(5^2)$

Now, calculate:

$3^2 = 9$ $5^2 = 25$ $2(9) = 18$ $3(25) = 75$ $18 + 75 = 93$

So, the value of $2x^2 + 3y^2$ is $93$.

Summary

a) $4x - 2y = 2$

b) $2x^2 + 3y^2 = 93$

Would you like more details or have any questions?

Here are some related questions for further practice:

1. What is the value of $5x + 3y$ when $x = 3$ and $y = 5$?
2. How do you simplify $x^2 + y^2$ for $x = 3$ and $y = 5$?
3. Find the value of $6x - 4y + 2$ when $x = 3$ and $y = 5$.
4. What is the value of $\frac{4x}{2y}$ with $x = 3$ and $y = 5$?
5. Calculate $x^3 + y^3$ for $x = 3$ and $y = 5$.

Tip: When evaluating algebraic expressions, always substitute the given values first and then follow the order of operations (PEMDAS/BODMAS).