Factor. 4u^2 - 9 ______

Determine factoring technique: Determine the appropriate factoring technique for 4u^2 - 9. Since we have a difference of squares, we can use the identity (a^2 - b^2) = (a + b)(a - b).Identify terms as squares: Identify the terms in the expression 4u^2 - 9 as squares. 4u^2 can be written as (2u)^2 because 2u * 2u = 4u^2. 9 can be written as 3^2 because 3 * 3 = 9. So, 4u^2 - 9 is in the form of a^2 - b^2 where a = 2u and b = 3.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: (2u)^2 - 3^2 = (2u + 3)(2u - 3).Write final factored form: Write the final factored form of the expression. The factored form of 4u^2 - 9 is (2u + 3)(2u - 3).

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Algebra 1

Factor quadratics: special cases

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Q. Factor.

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4u^2 - 9

Determine factoring technique: Determine the appropriate factoring technique for $4u^2 - 9$ . Since we have a difference of squares, we can use the identity $(a^2 - b^2) = (a + b)(a - b)$ .
Identify terms as squares: Identify the terms in the expression $4u^2 - 9$ as squares. $\newline$ $4u^2$ can be written as $(2u)^2$ because $2u \times 2u = 4u^2$ . $\newline$ $9$ can be written as $3^2$ because $3 \times 3 = 9$ . $\newline$ So, $4u^2 - 9$ is in the form of $a^2 - b^2$ where $a = 2u$ and $4u^2$ $0$ .
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: $\newline$ $(2u)^2 - 3^2 = (2u + 3)(2u - 3)$ .
Write final factored form: Write the final factored form of the expression. $\newline$ The factored form of $4u^2 - 9$ is $(2u + 3)(2u - 3)$ .