Factor completely: 64w^(9)-s^(9) Answer:

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Factor completely:  64w^(9)-s^(9) Answer:

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Recognize Difference of Cubes: Step Title: Recognize the Difference of Two Cubes Concise Step Description: Identify that the expression is a difference of two cubes. Step Calculation: The expression 64w^9 - s^9 can be written as (4w^3)^3 - (s^3)^3, which is a difference of two cubes. Step Output: Expression rewritten as a difference of two cubes.Apply Cubes Formula: Step Title: Apply the Difference of Two Cubes Formula Concise Step Description: Use the formula a^3 - b^3 = (a - b)(a^2 + ab + b^2) to factor the expression. Step Calculation: Let a = 4w^3 and b = s^3. Then, apply the formula to get (4w^3 - s^3)((4w^3)^2 + (4w^3)(s^3) + (s^3)^2). Step Output: Factored expression using the difference of two cubes formula.Simplify Factored Expression: Step Title: Simplify the Factored Expression Concise Step Description: Simplify the terms in the factored expression. Step Calculation: Simplify (4w^3 - s^3)(16w^6 + 4w^3s^3 + s^6). Step Output: Simplified factored expression.Check Further Factoring: Step Title: Check for Further Factoring Concise Step Description: Check if the terms (4w^3 - s^3) and (16w^6 + 4w^3s^3 + s^6) can be factored further. Step Calculation: The term (4w^3 - s^3) is a difference of cubes again and can be factored further. The term (16w^6 + 4w^3s^3 + s^6) cannot be factored further. Step Output: Determination that (4w^3 - s^3) can be factored further.Factor Cubes Again: Step Title: Factor the Difference of Cubes Again Concise Step Description: Apply the difference of cubes formula to the term (4w^3 - s^3). Step Calculation: Let a = 4w and b = s. Then, apply the formula to get (4w - s)((4w)^2 + (4w)(s) + s^2). Step Output: Factored expression (4w - s)(16w^2 + 4ws + s^2).Combine Factored Terms: Step Title: Combine All Factored Terms Concise Step Description: Combine the factored terms to write the final factored expression. Step Calculation: The final factored expression is (4w - s)(16w^2 + 4ws + s^2)(16w^6 + 4w^3s^3 + s^6). Step Output: Final factored expression.

Factor completely: $\newline$ $64 w^{9}-s^{9}$ $\newline$ Answer:

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Factor completely: $\newline$ $64 w^{9}-s^{9}$ $\newline$ Answer: