To square the binomial [tex]\((8y - 5)^2\)[/tex], we use the formula for the square of a binomial [tex]\((a - b)^2\)[/tex]. The formula is given by:
[tex]\[
(a - b)^2 = a^2 - 2ab + b^2
\][/tex]
Here, [tex]\(a = 8y\)[/tex] and [tex]\(b = 5\)[/tex].
1. Square the first term:
[tex]\[
a^2 = (8y)^2 = 64y^2
\][/tex]
2. Multiply the first term by the second term and then by 2:
[tex]\[
-2ab = -2 \cdot (8y) \cdot 5 = -80y
\][/tex]
3. Square the second term:
[tex]\[
b^2 = 5^2 = 25
\][/tex]
Now, combining these results, we get:
[tex]\[
(8y - 5)^2 = 64y^2 - 80y + 25
\][/tex]
So the expanded form of the binomial [tex]\((8y - 5)^2\)[/tex] is:
[tex]\[
64y^2 - 80y + 25
\][/tex]
Thus, the correct answer is:
[tex]\[
64y^2 - 80y + 25
\][/tex]
