Certainly! Let's simplify and solve the expression [tex]\((7n - 8n)^2\)[/tex] step by step.
1. Combine Like Terms Inside the Parentheses:
- The expression inside the parentheses is [tex]\(7n - 8n\)[/tex].
- Combine the like terms: [tex]\(7n - 8n = (7 - 8)n = -1n = -n\)[/tex].
2. Square the Simplified Expression:
- Now that we have [tex]\(-n\)[/tex] inside the parentheses, we need to square this expression.
- [tex]\((-n)^2 = (-1 \cdot n)^2\)[/tex].
3. Calculate the Square:
- Squaring [tex]\(-1\)[/tex] gives [tex]\(1\)[/tex].
- Squaring [tex]\(n\)[/tex] gives [tex]\(n^2\)[/tex].
- Therefore, [tex]\((-1n)^2 = 1 \cdot n^2 = n^2\)[/tex].
Thus, the simplified and final result of the given expression [tex]\((7n - 8n)^2\)[/tex] is [tex]\(n^2\)[/tex].
[tex]\[
(7n - 8n)^2 = n^2
\][/tex]
