Factor completely: r^(9)-z^(9) Answer:

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Factor completely:  r^(9)-z^(9) Answer:

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Identify Expression Type: Step Title: Identify the Type of Expression Concise Step Description: Recognize that the expression is a difference of two powers. Step Calculation: The expression is r^(9) - z^(9), which is a difference of two ninth powers.Apply Squares Formula: Step Title: Apply the Difference of Two Squares Formula Concise Step Description: Use the difference of two squares formula, a^2 - b^2 = (a + b)(a - b), to factor the expression. Step Calculation: The expression can be written as (r^(9/2))^2 - (z^(9/2))^2, which is a difference of squares.Factor Using Cubes Formulas: Step Title: Factor Using the Sum and Difference of Cubes Formulas Concise Step Description: Recognize that the expression can be further factored using the sum and difference of cubes formulas, a^3 - b^3 = (a - b)(a^2 + ab + b^2) and a^3 + b^3 = (a + b)(a^2 - ab + b^2). Step Calculation: The expression (r^(9/2))^2 - (z^(9/2))^2 can be factored as (r^(9/2) - z^(9/2))(r^(9/2) + z^(9/2)).Recognize Difference of Cubes: Step Title: Recognize the Difference of Cubes Concise Step Description: Notice that r^(9/2) - z^(9/2) is a difference of cubes, as (r^(3))^3 - (z^(3))^3. Step Calculation: Factor r^(9/2) - z^(9/2) using the difference of cubes formula to get (r^3 - z^3)(r^6 + r^3z^3 + z^6).Factor Cubes Completely: Step Title: Factor the Difference of Cubes Completely Concise Step Description: Factor r^3 - z^3 completely using the difference of cubes formula. Step Calculation: Factor r^3 - z^3 to get (r - z)(r^2 + rz + z^2).Combine All Factors: Step Title: Combine All Factors Concise Step Description: Combine all the factors obtained from the previous steps to write the final factored form of the original expression. Step Calculation: The final factored form is (r - z)(r^2 + rz + z^2)(r^3 + z^3)(r^3 - z^3).

Factor completely: $\newline$ $r^{9}-z^{9}$ $\newline$ Answer:

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Factor completely: $\newline$ $r^{9}-z^{9}$ $\newline$ Answer: