Factor completely: w^(6)-1 Answer:

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Factor completely:  w^(6)-1 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 - 1 is a difference of squares because it can be written as (w^3)^2 - 1^2. Step Output: Difference of squares: (w^3)^2 - 1^2Apply 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: Apply the formula with a = w^3 and b = 1 to get (w^3 + 1)(w^3 - 1). Step Output: Factored form: (w^3 + 1)(w^3 - 1)Factor Further if Possible: Step Title: Factor Further if Possible Concise Step Description: Check if the resulting binomials can be factored further, especially the w^3 - 1 term, which is also a difference of cubes. Step Calculation: Recognize that w^3 - 1 is a difference of cubes and can be factored using the formula a^3 - b^3 = (a - b)(a^2 + ab + b^2) with a = w and b = 1. Step Output: Factored form of w^3 - 1: (w - 1)(w^2 + w + 1)Combine Factored Forms: Step Title: Combine Factored Forms Concise Step Description: Combine the factored forms from the previous steps to write the completely factored expression. Step Calculation: The completely factored form is (w^3 + 1)(w - 1)(w^2 + w + 1). Step Output: Completely factored form: (w^3 + 1)(w - 1)(w^2 + w + 1)

Factor completely: $\newline$ $w^{6}-1$ $\newline$ Answer:

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Factor completely: $\newline$ $w^{6}-1$ $\newline$ Answer: