Sure! Let's expand and simplify the expression [tex]\((5v - 6)^2\)[/tex].
### Step-by-Step Solution:
1. Start with the given expression:
[tex]\[
(5v - 6)^2
\][/tex]
2. Use the algebraic identity for the square of a binomial:
[tex]\[
(a - b)^2 = a^2 - 2ab + b^2
\][/tex]
Here, [tex]\(a = 5v\)[/tex] and [tex]\(b = 6\)[/tex].
3. Apply the identity:
[tex]\[
(5v - 6)^2 = (5v)^2 - 2 \cdot (5v) \cdot 6 + 6^2
\][/tex]
4. Calculate each term:
- First term:
[tex]\[
(5v)^2 = 25v^2
\][/tex]
- Second term:
[tex]\[
-2 \cdot (5v) \cdot 6 = -60v
\][/tex]
- Third term:
[tex]\[
6^2 = 36
\][/tex]
5. Combine all the terms:
[tex]\[
(5v - 6)^2 = 25v^2 - 60v + 36
\][/tex]
Thus, the expanded and simplified form of [tex]\((5v - 6)^2\)[/tex] is:
[tex]\[
25v^2 - 60v + 36
\][/tex]
