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What is the value of [tex]\(m^2 - 2mn + n^2\)[/tex] for [tex]\(m = -2\)[/tex] and [tex]\(n = 4\)[/tex]?

A. [tex]\(-36\)[/tex]

B. [tex]\(-4\)[/tex]

C. 4

D. 36


Sagot :

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].
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