Multiply the binomials.
$(y+\frac{1}{8})(y-\frac{1}{8})$

• A. $y^2-\frac{1}{4}y-\frac{1}{64}$
• B. $y^2+\frac{1}{4}y-\frac{1}{64}$
• C. $y^2-\frac{1}{64}$
• D. $y^2+\frac{1}{64}$

Answer: (C)

Verified step by step guidance

1. Identify the binomials to multiply: \(\left(y+\frac{1}{8}\right)\left(y-\frac{1}{8}\right)\).
2. Recognize that this is a product of conjugates, which follows the pattern \(\left(a+b\right)\left(a-b\right) = a^2 - b^2\).
3. Apply the pattern by letting \(a = y\) and \(b = \frac{1}{8}\), so the product becomes \(y^2 - \left(\frac{1}{8}\right)^2\).
4. Square each term: \(y^2\) remains \(y^2\), and \(\left(\frac{1}{8}\right)^2\) becomes \(\frac{1}{64}\).
5. Write the final expression as \(y^2 - \frac{1}{64}\), which is the simplified product of the binomials.