Factor. 25n^2 - 40n + 16 ______

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Determine Factoring Possibility: Determine if the quadratic can be factored using the form (an - b)^2 = a^2n^2 - 2abn + b^2. We notice that 25n^2 is a perfect square, as is 16. The middle term is -40n, which could be the result of 2 times the product of the square roots of 25n^2 and 16. Let's check if this is a perfect square trinomial: (5n)^2 = 25n^2 (which matches the first term), (4)^2 = 16 (which matches the third term), 2 * 5n * 4 = 40n (which matches the middle term, but we need to consider the sign). Since the middle term is negative, we are looking for (5n - 4)^2.Write as Square of Binomial: Write the quadratic as a square of a binomial. The quadratic 25n^2 - 40n + 16 can be written as (5n - 4)^2 because it matches the form a^2n^2 - 2abn + b^2 with a = 5n and b = 4.Check Factored Form: Check the factored form by expanding (5n - 4)^2 to ensure it equals the original quadratic. (5n - 4)^2 = (5n - 4)(5n - 4) = 25n^2 - 20n - 20n + 16 = 25n^2 - 40n + 16. This matches the original quadratic, confirming that the factored form is correct.

Factor. $\newline$ $25n^2 - 40n + 16$

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Factor.\newline25n2−40n+1625n^2 - 40n + 1625n2−40n+16

Factor. $\newline$ $25n^2 - 40n + 16$