Factor. 9s^2 - 4 ______

Identify Factoring Technique: Determine the appropriate factoring technique for 9s^2 - 4. Since we have a difference of squares, we can use the identity (a^2 - b^2) = (a + b)(a - b).Express as Difference of Squares: Express 9s^2 - 4 as a difference of squares. 9s^2 can be written as (3s)^2 because 3s * 3s = 9s^2. 4 can be written as 2^2 because 2 * 2 = 4. So, 9s^2 - 4 is in the form of a^2 - b^2 where a = 3s and b = 2.Apply Difference of Squares Formula: Apply the difference of squares formula to factor the expression. Using the identity (a^2 - b^2) = (a + b)(a - b), we get: (3s)^2 - 2^2 = (3s + 2)(3s - 2).Write Final Factored Form: Write the final factored form. The factored form of 9s^2 - 4 is (3s + 2)(3s - 2).

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Algebra 1

Factor quadratics: special cases

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Q. Factor.

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9s^2 - 4

Identify Factoring Technique: Determine the appropriate factoring technique for $9s^2 - 4$ . Since we have a difference of squares, we can use the identity $(a^2 - b^2) = (a + b)(a - b)$ .
Express as Difference of Squares: Express $9s^2 - 4$ as a difference of squares. $\newline$ $9s^2$ can be written as $(3s)^2$ because $3s \times 3s = 9s^2$ . $\newline$ $4$ can be written as $2^2$ because $2 \times 2 = 4$ . $\newline$ So, $9s^2 - 4$ is in the form of $a^2 - b^2$ where $a = 3s$ and $9s^2$ $0$ .
Apply Difference of Squares Formula: Apply the difference of squares formula to factor the expression. $\newline$ Using the identity $(a^2 - b^2) = (a + b)(a - b)$ , we get: $\newline$ $(3s)^2 - 2^2 = (3s + 2)(3s - 2)$ .
Write Final Factored Form: Write the final factored form. $\newline$ The factored form of $9s^2 - 4$ is $(3s + 2)(3s - 2)$ .