Factor. 9n^2 - 25 ______

Determine Technique: Determine the appropriate factoring technique for 9n^2 - 25. Since we have a difference of squares, we can use the formula a^2 - b^2 = (a - b)(a + b).Express as Squares: Express 9n^2 - 25 as a difference of squares. 9n^2 can be written as (3n)^2 because 3n * 3n = 9n^2. 25 can be written as 5^2 because 5 * 5 = 25. So, 9n^2 - 25 is in the form of a^2 - b^2 where a = 3n and b = 5.Apply Formula: Apply the difference of squares formula to factor the expression. Using the formula a^2 - b^2 = (a - b)(a + b), we get: (3n)^2 - 5^2 = (3n - 5)(3n + 5).

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Algebra 1

Factor quadratics: special cases

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Q. Factor.

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9n^2 - 25

Determine Technique: Determine the appropriate factoring technique for $9n^2 - 25$ . Since we have a difference of squares, we can use the formula $a^2 - b^2 = (a - b)(a + b)$ .
Express as Squares: Express $9n^2 - 25$ as a difference of squares. $\newline$ $9n^2$ can be written as $(3n)^2$ because $3n \times 3n = 9n^2$ . $\newline$ $25$ can be written as $5^2$ because $5 \times 5 = 25$ . $\newline$ So, $9n^2 - 25$ is in the form of $a^2 - b^2$ where $a = 3n$ and $9n^2$ $0$ .
Apply Formula: Apply the difference of squares formula to factor the expression. $\newline$ Using the formula $a^2 - b^2 = (a - b)(a + b)$ , we get: $\newline$ $(3n)^2 - 5^2 = (3n - 5)(3n + 5)$ .