Factor completely: b^(9)-1 Answer:

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Factor completely:  b^(9)-1 Answer:

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Recognize Difference of Two Squares: Step Title: Recognize the Difference of Two Squares Concise Step Description: Identify that the expression is a difference of two squares, which can be factored as (a^2 - b^2) = (a - b)(a + b). Step Calculation: Recognize that b^9 is (b^3)^3 and 1 is 1^3, so the expression can be written as (b^3)^3 - 1^3. Step Output: Expression is a difference of two squares.Apply Squares Formula: Step Title: Apply the Difference of Two Squares Formula Concise Step Description: Apply the difference of two squares formula to factor the expression. Step Calculation: Factor b^9 - 1 as (b^3 - 1)(b^3 + 1). Step Output: Factored form is (b^3 - 1)(b^3 + 1).Factor First Term Further: Step Title: Factor the First Term Further Concise Step Description: Recognize that the first term (b^3 - 1) is also a difference of two squares and can be factored further. Step Calculation: Factor b^3 - 1 as (b - 1)(b^2 + b + 1). Step Output: Factored form of the first term is (b - 1)(b^2 + b + 1).Factor Second Term Further: Step Title: Factor the Second Term Further Concise Step Description: Recognize that the second term (b^3 + 1) is a sum of two cubes and can be factored using the sum of cubes formula. Step Calculation: Factor b^3 + 1 as (b + 1)(b^2 - b + 1). Step Output: Factored form of the second term is (b + 1)(b^2 - b + 1).Combine Factored Forms: Step Title: Combine the Factored Forms Concise Step Description: Combine the factored forms of both terms to get the completely factored expression. Step Calculation: The completely factored form is (b - 1)(b^2 + b + 1)(b + 1)(b^2 - b + 1). Step Output: Completely factored form is (b - 1)(b^2 + b + 1)(b + 1)(b^2 - b + 1).

Factor completely: $\newline$ $b^{9}-1$ $\newline$ Answer:

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Factor completely: $\newline$ $b^{9}-1$ $\newline$ Answer: