Factor. 25s^2 - 1 ______

Determine method: Determine the appropriate method to factor 25s^2 - 1. Since we have a subtraction of two squares, we can use the difference of squares formula: (a^2 - b^2) = (a + b)(a - b).Identify expression: Identify 25s^2 - 1 in the form of a^2 - b^2. 25s^2 can be written as (5s)^2 because 5s * 5s = 25s^2. 1 can be written as 1^2 because 1 * 1 = 1. So, 25s^2 - 1 = (5s)^2 - 1^2.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: (5s)^2 - 1^2 = (5s + 1)(5s - 1).

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Factor. $\newline$ $25s^2 - 1$

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Algebra 1

Factor quadratics: special cases

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Q. Factor.

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25s^2 - 1

Determine method: Determine the appropriate method to factor $25s^2 - 1$ . Since we have a subtraction of two squares, we can use the difference of squares formula: $(a^2 - b^2) = (a + b)(a - b)$ .
Identify expression: Identify $25s^2 - 1$ in the form of $a^2 - b^2$ . $\newline$ $25s^2$ can be written as $(5s)^2$ because $5s \times 5s = 25s^2$ . $\newline$ $1$ can be written as $1^2$ because $1 \times 1 = 1$ . $\newline$ So, $25s^2 - 1 = (5s)^2 - 1^2$ .
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: $\newline$ $(5s)^2 - 1^2 = (5s + 1)(5s - 1)$ .