Factor completely. 49p^(8)+42p^(4)+9=

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Factor completely.  49p^(8)+42p^(4)+9=

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Identify Coefficients: Step Title: Identify the Coefficients Concise Step Description: Identify the coefficients of the given cubic expression. Step Calculation: Coefficients are 49, 42, and 9. Step Output: Coefficients: 49, 42, 9Look for Common Factor: Step Title: Look for a Common Factor Concise Step Description: Check if there is a common factor that can be factored out from all terms of the expression. Step Calculation: The greatest common factor of 49, 42, and 9 is 1. Step Output: No common factor other than 1.Recognize the Pattern: Step Title: Recognize the Pattern Concise Step Description: Recognize if the expression fits a special factoring pattern such as a perfect square trinomial or a sum of cubes. Step Calculation: The expression 49p^8 + 42p^4 + 9 resembles a perfect square trinomial a^2 + 2ab + b^2, where a = 7p^4 and b = 3. Step Output: Possible perfect square trinomial pattern.Factor as Perfect Square Trinomial: Step Title: Factor as a Perfect Square Trinomial Concise Step Description: Factor the expression as a perfect square trinomial if it fits the pattern. Step Calculation: The factored form is (7p^4 + 3)^2 because (7p^4)^2 = 49p^8, 2*(7p^4)*3 = 42p^4, and 3^2 = 9. Step Output: Factored Form: (7p^4 + 3)^2

Factor completely. $\newline$ $49 p^{8}+42 p^{4}+9=$

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Factor completely.\newline49p8+42p4+9= 49 p^{8}+42 p^{4}+9= 49p8+42p4+9=

Factor completely. $\newline$ $49 p^{8}+42 p^{4}+9=$