In various technical and mathematical applications, recognizing algebraic patterns is key to simplifying complex formulas. Which of the following is the correctly factored form of the expression ${}64y^2 - 1$?

An HVAC technician is analyzing the airflow through a duct system and encounters the expression ${}64y^2 - 1$ within a larger efficiency formula. To simplify the formula, the technician must factor this expression using the difference of squares pattern. Arrange the steps of the factoring process in the correct order as described in the course materials.

A manufacturing technician is simplifying a design formula that includes the expression ${}64y^2 - 1$. To factor this expression, the technician uses the difference of squares pattern: $a^2 - b^2 = (a - b)(a + b)$. Match each component of the pattern to its correct value for this specific expression.

A project manager is analyzing a budget spreadsheet that uses the algebraic expression ${}64y^2 - 1$. To simplify the model, the manager factors the expression. True or False: The expression ${}64y^2 - 1$ factors correctly into $(8y - 1)(8y + 1)$.

A data analyst for a retail company is reviewing an algebraic model used to predict seasonal inventory. A key part of the model contains the expression ${}64y^2 - 1$. To simplify the calculation, the analyst must factor the expression into two binomials. If one of the factors is $(8y - 1)$, the other factor is ____.