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

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Factor completely:  w^(6)-64 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 w^6 is a perfect square (w^3)^2 and 64 is a perfect square 8^2. Step Output: The expression can be written as (w^3)^2 - 8^2.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). Step Calculation: Factor the expression using the formula with a = w^3 and b = 8. Step Output: The factored form is (w^3 + 8)(w^3 - 8).Factor Further if Possible: Step Title: Factor Further if Possible Concise Step Description: Check if the resulting binomials can be factored further. Step Calculation: Recognize that w^3 - 8 is also a difference of cubes, which can be factored using the formula a^3 - b^3 = (a - b)(a^2 + ab + b^2). Step Output: Factor w^3 - 8 using the difference of cubes formula with a = w and b = 2.Apply Cubes Formula: Step Title: Apply the Difference of Cubes Formula Concise Step Description: Use the difference of cubes formula to factor w^3 - 8. Step Calculation: The factored form is (w - 2)(w^2 + 2w + 4). Step Output: The complete factored form is (w^3 + 8)(w - 2)(w^2 + 2w + 4).Check for Further Factoring: Step Title: Check for Further Factoring Concise Step Description: Verify if the remaining terms can be factored further. Step Calculation: Check if w^3 + 8 can be factored as a sum of cubes. Step Output: Recognize that w^3 + 8 is a sum of cubes, which can be factored using the formula a^3 + b^3 = (a + b)(a^2 - ab + b^2).Apply Sum of Cubes Formula: Step Title: Apply the Sum of Cubes Formula Concise Step Description: Use the sum of cubes formula to factor w^3 + 8. Step Calculation: The factored form is (w + 2)(w^2 - 2w + 4). Step Output: The completely factored form is (w + 2)(w^2 - 2w + 4)(w - 2)(w^2 + 2w + 4).

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

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Factor completely:\newlinew6−64 w^{6}-64 w6−64\newlineAnswer:

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