Certainly! Let's evaluate the given expression step-by-step when [tex]\( m = 4 \)[/tex] and [tex]\( n = 2 \)[/tex].
The expression to evaluate is:
[tex]\[ 3n + 2(2n + m) + m^2 \][/tex]
1. Substitute [tex]\( n = 2 \)[/tex] and [tex]\( m = 4 \)[/tex] into the expression:
[tex]\[ 3(2) + 2(2(2) + 4) + 4^2 \][/tex]
2. Compute the first part of the expression [tex]\( 3n \)[/tex]:
[tex]\[ 3(2) = 6 \][/tex]
3. Compute the inside of the second part [tex]\( 2(2n + m) \)[/tex]:
- First, compute [tex]\( 2n \)[/tex]:
[tex]\[ 2(2) = 4 \][/tex]
- Then add [tex]\( m \)[/tex]:
[tex]\[ 4 + 4 = 8 \][/tex]
- Multiply by 2:
[tex]\[ 2(8) = 16 \][/tex]
4. Compute the third part of the expression [tex]\( m^2 \)[/tex]:
[tex]\[ 4^2 = 16 \][/tex]
5. Add all parts together:
- First part:
[tex]\[ 6 \][/tex]
- Second part:
[tex]\[ 16 \][/tex]
- Third part:
[tex]\[ 16 \][/tex]
- Sum them:
[tex]\[ 6 + 16 + 16 = 38 \][/tex]
So, the evaluated result for [tex]\( 3n + 2(2n + m) + m^2 \)[/tex] when [tex]\( m = 4 \)[/tex] and [tex]\( n = 2 \)[/tex] is:
[tex]\[ 38 \][/tex]
