Square the binomial: [tex]\((8y - 5)^2\)[/tex]

A. [tex]\(64y^2 - 40y + 25\)[/tex]
B. [tex]\(64y^2 + 25\)[/tex]
C. [tex]\(64y^2 - 80y + 25\)[/tex]
D. [tex]\(64y^2 + 80y - 25\)[/tex]



Answer :

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]