Factor completely. 144-x^(6) Answer:

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Factor completely.  144-x^(6) 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 two binomials. Step Calculation: Recognize that $144 - x^6$ can be written as $ (12)^2 - (x^3)^2 $. Step Output: Expression as a difference of squares: $ (12)^2 - (x^3)^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) $, to factor the expression. Step Calculation: Apply the formula with $ a = 12 $ and $ b = x^3 $ to get $ (12 + x^3)(12 - x^3) $. Step Output: Factored form using the difference of squares: $ (12 + x^3)(12 - x^3) $Factor Further if Possible: Step Title: Factor Further if Possible Concise Step Description: Check if the resulting binomials can be factored further. Step Calculation: Notice that $12 - x^3$ is also a difference of cubes, which can be factored further using the formula $ a^3 - b^3 = (a - b)(a^2 + ab + b^2) $. However, $12 + x^3$ is a sum of cubes and does not factor over the integers. Step Output: No further factoring is possible for $12 + x^3$, but $12 - x^3$ can be factored further.Factor Difference of Cubes: Step Title: Factor the Difference of Cubes Concise Step Description: Use the difference of cubes formula to factor $12 - x^3$. Step Calculation: Apply the formula with $ a = 12 $ and $ b = x $ to get $ (12 - x)(144 + 12x + x^2) $. Step Output: Factored form using the difference of cubes: $ (12 - x)(144 + 12x + x^2) $Combine Factored Forms: Step Title: Combine Factored Forms Concise Step Description: Combine the factored forms to express the original expression completely factored. Step Calculation: Combine the factored forms to get $ (12 + x^3)(12 - x)(144 + 12x + x^2) $. Step Output: Completely factored form: $ (12 + x^3)(12 - x)(144 + 12x + x^2) $

Factor completely. $\newline$ $144-x^{6}$ $\newline$ Answer:

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Factor completely. $\newline$ $144-x^{6}$ $\newline$ Answer: