Factor. 9w^2 - 4 ______

Determine factoring technique: Determine the appropriate factoring technique for 9w^2 - 4. Since we have a subtraction of two squares, we can use the difference of squares formula, which is a^2 - b^2 = (a + b)(a - b).Identify squares in expression: Identify the terms in the expression 9w^2 - 4 as squares. 9w^2 can be written as (3w)^2 because 3w * 3w = 9w^2. 4 can be written as 2^2 because 2 * 2 = 4. So, 9w^2 - 4 is in the form of a^2 - b^2 where a = 3w and b = 2.Apply difference of squares formula: Apply the difference of squares formula to factor the expression. Using the formula a^2 - b^2 = (a - b)(a + b), we substitute a with 3w and b with 2. (3w)^2 - 2^2 = (3w - 2)(3w + 2)Write final factored form: Write the final factored form of the expression. The factored form of 9w^2 - 4 is (3w - 2)(3w + 2).

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Algebra 1

Factor quadratics: special cases

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Q. Factor.

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9w^2 - 4

Determine factoring technique: Determine the appropriate factoring technique for $9w^2 - 4$ . Since we have a subtraction of two squares, we can use the difference of squares formula, which is $a^2 - b^2 = (a + b)(a - b)$ .
Identify squares in expression: Identify the terms in the expression $9w^2 - 4$ as squares. $\newline$ $9w^2$ can be written as $(3w)^2$ because $3w \times 3w = 9w^2$ . $\newline$ $4$ can be written as $2^2$ because $2 \times 2 = 4$ . $\newline$ So, $9w^2 - 4$ is in the form of $a^2 - b^2$ where $a = 3w$ and $9w^2$ $0$ .
Apply difference of squares formula: Apply the difference of squares formula to factor the expression. $\newline$ Using the formula $a^2 - b^2 = (a - b)(a + b)$ , we substitute $a$ with $3w$ and $b$ with $2$ . $\newline$ $(3w)^2 - 2^2 = (3w - 2)(3w + 2)$
Write final factored form: Write the final factored form of the expression. $\newline$ The factored form of $9w^2 - 4$ is $(3w - 2)(3w + 2)$ .