Question

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Explanation:

Identify the given expression

The given expression to factor completely is:

$$ 36y^2 - 1 $$

Recognize the algebraic pattern

The expression is a binomial of the form \(a^2 - b^2\), which represents a difference of squares:

$$ a^2 - b^2 = (a + b)(a - b) $$

Here, we can rewrite each term as a perfect square:

$$ 36y^2 = (6y)^2 $$

$$ 1 = (1)^2 $$

Apply the factorization formula

Substitute \(a = 6y\) and \(b = 1\) into the difference of squares formula:

$$ (6y)^2 - (1)^2 = (6y + 1)(6y - 1) $$

Answer:

• (A) \((6y + 1)(y - 1)\)
• (B) \((6y + 1)(6y - 1)\) (Correct answer)
• (C) \((6y - 1)^2\)
• (D) \((y - 6)(y + 6)\)