Sure! Let's evaluate the expression [tex]\( 2y + 3(x - y) + x^2 \)[/tex] step by step, given [tex]\( x = 3 \)[/tex] and [tex]\( y = 5 \)[/tex].
1. Substitute the given values:
[tex]\[
x = 3, \quad y = 5
\][/tex]
2. Break down the expression into individual terms:
[tex]\[
\text{Expression} = 2y + 3(x - y) + x^2
\][/tex]
3. Evaluate each term one by one:
- First term: [tex]\( 2y \)[/tex]
[tex]\[
2y = 2 \times 5 = 10
\][/tex]
- Second term: [tex]\( 3(x - y) \)[/tex]
[tex]\[
x - y = 3 - 5 = -2
\][/tex]
Then,
[tex]\[
3(x - y) = 3 \times -2 = -6
\][/tex]
- Third term: [tex]\( x^2 \)[/tex]
[tex]\[
x^2 = 3^2 = 9
\][/tex]
4. Combine the evaluated terms:
[tex]\[
2y + 3(x - y) + x^2 = 10 + (-6) + 9
\][/tex]
5. Add the values:
[tex]\[
10 - 6 + 9 = 13
\][/tex]
So, the value of the expression [tex]\( 2y + 3(x - y) + x^2 \)[/tex] when [tex]\( x = 3 \)[/tex] and [tex]\( y = 5 \)[/tex] is:
[tex]\[
\boxed{13}
\][/tex]
