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Factor completely. 4n2−254n^2-25

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Full solution

Q. Factor completely. 4n2−254n^2-25
  1. Recognize as difference of squares: Recognize the expression as a difference of squares. A difference of squares is a binomial of the form a2−b2a^2 - b^2, which factors into (a+b)(a−b)(a + b)(a - b). The expression 4n2–254n^2 – 25 can be written as (2n)2−(5)2(2n)^2 - (5)^2, which fits the form a2−b2a^2 - b^2 with a=2na = 2n and b=5b = 5.
  2. Apply formula for factoring: Apply the difference of squares formula. Using the formula (a2−b2)=(a+b)(a−b)(a^2 - b^2) = (a + b)(a - b), we can factor the expression as follows: (2n+5)(2n−5)(2n + 5)(2n - 5).

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