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Factor completely.

121c^(4)-44c^(2)+4=

Factor completely.\newline121c444c2+4= 121 c^{4}-44 c^{2}+4=

Full solution

Q. Factor completely.\newline121c444c2+4= 121 c^{4}-44 c^{2}+4=
  1. Identify Structure of Expression: Step Title: Identify the Structure of the Expression\newlineConcise Step Description: Recognize that the given expression is a quadratic in terms of c2c^2.\newlineStep Calculation: The expression is in the form of a quadratic equation, where the variable is c2c^2 instead of cc.\newlineStep Output: The expression is a quadratic in c2c^2.
  2. Identify Coefficients: Step Title: Identify the Coefficients\newlineConcise Step Description: Identify the coefficients of the quadratic equation in terms of c2c^2.\newlineStep Calculation: Coefficients are 121121, 44-44, and 44.\newlineStep Output: Coefficients: 121121, 44-44, 44
  3. Find Factors: Step Title: Find the Factors\newlineConcise Step Description: Find two numbers that multiply to 44 (the last term) and add to 44-44 (the coefficient of the middle term), considering the first term coefficient is 121121.\newlineStep Calculation: Factors of 44 that add up to 44-44 when multiplied by 121121 are 2-2 and 2-2 (since 121×4=484121 \times 4 = 484, and we need two numbers that multiply to 484484 and add up to 44-44).\newlineStep Output: Factors: 2-2, 2-2
  4. Write Factored Form: Step Title: Write the Factored Form\newlineConcise Step Description: Write the factored form of the quadratic equation using the factors found in the previous step.\newlineStep Calculation: The factored form is (11c22)(11c22)(11c^2 - 2)(11c^2 - 2), which is a perfect square trinomial.\newlineStep Output: Factored Form: (11c22)2(11c^2 - 2)^2