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Factor completely: 25x^(2)(x-5)-(x-5) Answer:

Factor completely:\newline25x2(x−5)−(x−5) 25 x^{2}(x-5)-(x-5) \newlineAnswer:

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Estimate positive square rootsright chevron icon

Full solution

Q. Factor completely:\newline25x2(x−5)−(x−5) 25 x^{2}(x-5)-(x-5) \newlineAnswer:
  1. Identify Common Factor: Identify the common factor in both terms.\newlineThe common factor in both terms is (x−5)(x-5).
  2. Factor Out Common Factor: Factor out the common factor (x−5)(x-5).\newlineThe expression can be rewritten as (x−5)(25x2−1)(x-5)(25x^2 - 1).
  3. Recognize Difference of Squares: Recognize that the second term is a difference of squares. 25x2−125x^2 - 1 can be factored as (5x+1)(5x−1)(5x + 1)(5x - 1) because it is a difference of squares where a2−b2=(a+b)(a−b)a^2 - b^2 = (a + b)(a - b).
  4. Write Final Factored Form: Write the final factored form.\newlineThe complete factorization of the expression is (x−5)(5x+1)(5x−1)(x-5)(5x + 1)(5x - 1).

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