To find the value of the expression 2x² + 3xy + 4y² when x = 2 and y = 4, we will substitute the values of x and y into the expression.
First, substitute x and y:
1. Calculate 2x²:
- 2(2)² = 2(4) = 8
2. Calculate 3xy:
- 3(2)(4) = 3(8) = 24
3. Calculate 4y²:
- 4(4)² = 4(16) = 64
Now, we add these results together:
- 8 + 24 + 64 = 96
Therefore, the value of the expression 2x² + 3xy + 4y² when x = 2 and y = 4 is 96.