Sure, let's evaluate the expression step-by-step with the given values. The expression we need to evaluate is [tex]\(2y + 3(x - y) + x^2\)[/tex].
Given:
[tex]\[ x = 3 \][/tex]
[tex]\[ y = 5 \][/tex]
Now, let's substitute these values into the expression and simplify step-by-step.
1. Substitute [tex]\( x = 3 \)[/tex] and [tex]\( y = 5 \)[/tex] into the expression:
[tex]\[ 2y + 3(x - y) + x^2 \][/tex]
[tex]\[ 2(5) + 3(3 - 5) + 3^2 \][/tex]
2. Simplify inside the parentheses first:
[tex]\[ 2(5) + 3(-2) + 3^2 \][/tex]
3. Calculate the multipliers and exponentiation:
[tex]\[ 10 + 3(-2) + 9 \][/tex]
4. Perform the multiplication:
[tex]\[ 10 - 6 + 9 \][/tex]
5. Finally, perform the addition and subtraction from left to right:
[tex]\[ 10 - 6 = 4 \][/tex]
[tex]\[ 4 + 9 = 13 \][/tex]
Therefore, the result of evaluating the expression [tex]\(2y + 3(x - y) + x^2 \)[/tex] when [tex]\( x = 3 \)[/tex] and [tex]\( y = 5 \)[/tex] is:
[tex]\[ 13 \][/tex]
