Factor completely. 1-81x^(12) Answer:

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Factor completely.  1-81x^(12) Answer:

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Identify Factoring Type: Identify the type of factoring needed for the expression 1 - 81x^(12). The expression is a difference of squares because it can be written as 1^2 - (9x^6)^2, which fits the form a^2 - b^2.Apply Difference of Squares: Apply the difference of squares formula to factor the expression. The difference of squares formula is a^2 - b^2 = (a - b)(a + b). Here, a = 1 and b = 9x^6. So, 1 - 81x^(12) = (1 - 9x^6)(1 + 9x^6).Check Further Factoring: Check for further factoring possibilities. Both 1 - 9x^6 and 1 + 9x^6 are also differences of squares, since they can be written as 1^2 - (3x^3)^2 and 1^2 + (3x^3)^2, respectively.Factor 1 - 9x^6: Factor 1 - 9x^6 further using the difference of squares formula. 1 - 9x^6 = (1 - 3x^3)(1 + 3x^3).Factor 1 + 9x^6: Factor 1 + 9x^6 further using the sum of squares formula. However, the sum of squares formula does not result in real factors for polynomials. Therefore, 1 + 9x^6 cannot be factored further over the real numbers.Combine Factored Parts: Combine all the factored parts to write the final factored form of the original expression. The final factored form of 1 - 81x^(12) is (1 - 3x^3)(1 + 3x^3)(1 + 9x^6).

Factor completely. $\newline$ $1-81 x^{12}$ $\newline$ Answer:

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Factor completely. $\newline$ $1-81 x^{12}$ $\newline$ Answer: