Factor completely: 64-v^(6) Answer:

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Factor completely:  64-v^(6) Answer:

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Recognize Difference of Squares: Step Title: Recognize the Difference of Squares Concise Step Description: Identify that the expression is a difference of squares, which can be factored into the product of a sum and difference. Step Calculation: Recognize that $64 - v^6$ can be written as $8^2 - (v^3)^2$.Apply Squares Formula: Step Title: Apply the Difference of Squares Formula Concise Step Description: Use the difference of squares formula, which states that $a^2 - b^2 = (a + b)(a - b)$, to factor the expression. Step Calculation: Factor $64 - v^6$ into $(8 + v^3)(8 - v^3)$.Factor Further if Possible: Step Title: Factor Further if Possible Concise Step Description: Check if the resulting binomials can be factored further, recognizing that $8 - v^3$ is also a difference of cubes. Step Calculation: Factor $8 - v^3$ using the difference of cubes formula, which states that $a^3 - b^3 = (a - b)(a^2 + ab + b^2)$.Apply Cubes Formula: Step Title: Apply the Difference of Cubes Formula Concise Step Description: Use the difference of cubes formula to factor $8 - v^3$. Step Calculation: Factor $8 - v^3$ into $(2 - v)(4 + 2v + v^2)$.Combine Factored Forms: Step Title: Combine Factored Forms Concise Step Description: Combine the factored forms from the previous steps to write the final factored expression. Step Calculation: The final factored form is $(8 + v^3)(2 - v)(4 + 2v + v^2)$.

Factor completely: $\newline$ $64-v^{6}$ $\newline$ Answer:

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Factor completely: $\newline$ $64-v^{6}$ $\newline$ Answer: