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

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Factor completely:  64-y^(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. Step Calculation: Recognize that 64 is a perfect square (8^2) and y^6 is also a perfect square (y^3)^2. Step Output: 64 = (8^2), y^6 = (y^3)^2Apply Squares Formula: Step Title: Apply the Difference of Squares Formula Concise Step Description: Use the difference of squares formula, which is a^2 - b^2 = (a + b)(a - b). Step Calculation: Apply the formula to the expression 64 - y^6, which gives us (8 + y^3)(8 - y^3). Step Output: Factored form as a difference of squares: (8 + y^3)(8 - y^3)Recognize Further Difference of Squares: Step Title: Recognize the Further Difference of Squares Concise Step Description: Identify that the term (8 - y^3) can be further factored as a difference of cubes. Step Calculation: Recognize that 8 is a perfect cube (2^3) and y^3 is also a perfect cube (y^1)^3. Step Output: 8 = (2^3), y^3 = (y^1)^3Apply Cubes Formula: Step Title: Apply the Difference of Cubes Formula Concise Step Description: Use the difference of cubes formula, which is a^3 - b^3 = (a - b)(a^2 + ab + b^2). Step Calculation: Apply the formula to the expression (8 - y^3), which gives us (2 - y)(4 + 2y + y^2). Step Output: Factored form as a difference of cubes: (2 - y)(4 + 2y + y^2)Combine Factored Forms: Step Title: Combine the Factored Forms Concise Step Description: Combine the factored forms from the difference of squares and the difference of cubes. Step Calculation: The final factored form is (8 + y^3)(2 - y)(4 + 2y + y^2). Step Output: Final factored form: (8 + y^3)(2 - y)(4 + 2y + y^2)

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

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Factor completely:\newline64−y6 64-y^{6} 64−y6\newlineAnswer:

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