Factor completely. 16x^(6)-81=

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Factor completely.  16x^(6)-81=

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Recognize the 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 form (a^2 - b^2) = (a + b)(a - b). Step Calculation: Recognize that 16x^6 is a perfect square (4x^3)^2 and 81 is also a perfect square (9)^2. Step Output: The expression can be written as (4x^3)^2 - (9)^2.Apply the Difference of Squares Formula: Step Title: Apply the Difference of Squares Formula Concise Step Description: Use the difference of squares formula to factor the expression. Step Calculation: Factor the expression as (4x^3 + 9)(4x^3 - 9). Step Output: Factored form is (4x^3 + 9)(4x^3 - 9).Check for Further Factoring: Step Title: Check for Further Factoring Concise Step Description: Check if the resulting binomials can be factored further. Step Calculation: Notice that 4x^3 + 9 cannot be factored further as it is not a difference of squares. However, 4x^3 - 9 is a difference of squares and can be factored further. Step Output: The expression (4x^3 - 9) can be factored further.Factor the Remaining Difference of Squares: Step Title: Factor the Remaining Difference of Squares Concise Step Description: Factor the binomial (4x^3 - 9) which is a difference of squares. Step Calculation: Recognize that (4x^3 - 9) can be written as (2x)^3 - (3)^3, which is a difference of cubes, not squares. This requires using the difference of cubes formula: a^3 - b^3 = (a - b)(a^2 + ab + b^2). Step Output: Factored form is (2x - 3)((2x)^2 + (2x)(3) + (3)^2).Complete the Factoring of the Difference of Cubes: Step Title: Complete the Factoring of the Difference of Cubes Concise Step Description: Apply the difference of cubes formula to the expression (2x - 3)((2x)^2 + (2x)(3) + (3)^2). Step Calculation: The factored form is (2x - 3)(4x^2 + 6x + 9). Step Output: The completely factored form is (4x^3 + 9)(2x - 3)(4x^2 + 6x + 9).

Factor completely. $\newline$ $16 x^{6}-81=$

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Factor completely.\newline16x6−81= 16 x^{6}-81= 16x6−81=

Factor completely. $\newline$ $16 x^{6}-81=$