To solve the expression [tex]\((m - n)^2 - 3m + 3n + (m - n + 6)\)[/tex] given [tex]\(m = 8\)[/tex] and [tex]\(n = -2\)[/tex], we need to break it down step-by-step.
### Step 1: Calculate [tex]\((m - n)^2\)[/tex]
First, let's compute [tex]\(m - n\)[/tex]:
[tex]\[ m - n = 8 - (-2) = 8 + 2 = 10 \][/tex]
Now, we square this result:
[tex]\[ (m - n)^2 = 10^2 = 100 \][/tex]
So, [tex]\((m - n)^2 = 100\)[/tex].
### Step 2: Calculate [tex]\(-3m\)[/tex]
Next, we need to calculate [tex]\(-3\)[/tex] times [tex]\(m\)[/tex]:
[tex]\[ -3m = -3 \cdot 8 = -24 \][/tex]
So, [tex]\(-3m = -24\)[/tex].
### Step 3: Calculate [tex]\(3n\)[/tex]
Similarly, we calculate [tex]\(3\)[/tex] times [tex]\(n\)[/tex]:
[tex]\[ 3n = 3 \cdot (-2) = -6 \][/tex]
So, [tex]\(3n = -6\)[/tex].
### Step 4: Calculate [tex]\((m - n + 6)\)[/tex]
Then, we compute [tex]\(m - n + 6\)[/tex]:
[tex]\[ m - n + 6 = 10 + 6 = 16 \][/tex]
So, [tex]\(m - n + 6 = 16\)[/tex].
### Step 5: Sum all parts
Finally, sum all the parts we calculated:
[tex]\[ 100 + (-24) + (-6) + 16 \][/tex]
Breaking it down step-by-step:
[tex]\[ 100 - 24 = 76 \][/tex]
[tex]\[ 76 - 6 = 70 \][/tex]
[tex]\[ 70 + 16 = 86 \][/tex]
So, the final result for the expression [tex]\((m - n)^2 - 3m + 3n + (m - n + 6)\)[/tex] when [tex]\(m = 8\)[/tex] and [tex]\(n = -2\)[/tex] is:
[tex]\[
86
\][/tex]
