Sure, let's solve the expression step-by-step, given [tex]\( m = 8 \)[/tex] and [tex]\( n = -2 \)[/tex].
We need to evaluate the expression:
[tex]\[
(m - n)^2 - 3m + 3n + (m - n + 6)
\][/tex]
First, let's compute each part of the expression individually.
1. Calculate [tex]\( (m - n)^2 \)[/tex]:
[tex]\[
m - n = 8 - (-2) = 8 + 2 = 10
\][/tex]
[tex]\[
(m - n)^2 = 10^2 = 100
\][/tex]
2. Calculate [tex]\(-3m \)[/tex]:
[tex]\[
-3m = -3 \times 8 = -24
\][/tex]
3. Calculate [tex]\( 3n \)[/tex]:
[tex]\[
3n = 3 \times -2 = -6
\][/tex]
4. Calculate [tex]\( (m - n + 6) \)[/tex]:
[tex]\[
m - n = 10 \quad \text{(as calculated before)}
\][/tex]
[tex]\[
m - n + 6 = 10 + 6 = 16
\][/tex]
Now, add all the parts together:
[tex]\[
(m - n)^2 + (-3m) + 3n + (m - n + 6) = 100 + (-24) + (-6) + 16
\][/tex]
Combine the values:
[tex]\[
100 - 24 - 6 + 16 = 86
\][/tex]
So, the evaluated expression is:
[tex]\[
86
\][/tex]
