To find the value of the expression [tex]\(m^2 - 2mn + n^2\)[/tex] for [tex]\(m = -2\)[/tex] and [tex]\(n = 4\)[/tex], we can proceed as follows:
1. Substitute the given values of [tex]\(m\)[/tex] and [tex]\(n\)[/tex] into the expression:
- [tex]\(m = -2\)[/tex]
- [tex]\(n = 4\)[/tex]
2. Calculate each term in the expression:
- [tex]\(m^2 = (-2)^2 = 4\)[/tex]
- [tex]\(2mn = 2(-2)(4) = -16\)[/tex]
- [tex]\(n^2 = 4^2 = 16\)[/tex]
3. Substitute the calculated values back into the expression:
[tex]\[
m^2 - 2mn + n^2 = 4 - (-16) + 16
\][/tex]
4. Simplify the expression:
[tex]\[
4 + 16 + 16 = 36
\][/tex]
Therefore, the value of the expression [tex]\(m^2 - 2mn + n^2\)[/tex] for [tex]\(m = -2\)[/tex] and [tex]\(n = 4\)[/tex] is [tex]\(\boxed{36}\)[/tex].
