Factor. 4d^2 - 1 ______

Determine factoring technique: Determine the appropriate factoring technique for 4d^2 - 1. Since we have a difference of squares, we can use the formula a^2 - b^2 = (a - b)(a + b).Identify terms as squares: Identify the terms in the expression 4d^2 - 1 as squares. 4d^2 can be written as (2d)^2 because 2d * 2d = 4d^2. 1 can be written as 1^2 because 1 * 1 = 1. So, 4d^2 - 1 is in the form of a^2 - b^2 where a = 2d and b = 1.Apply difference of squares formula: Apply the difference of squares formula to factor the expression. Using a^2 - b^2 = (a - b)(a + b), we get: (2d)^2 - 1^2 = (2d - 1)(2d + 1).Write final factored form: Write the final factored form of the expression. The factored form of 4d^2 - 1 is (2d - 1)(2d + 1).

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Algebra 1

Factor quadratics: special cases

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Q. Factor.

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4d^2 - 1

Determine factoring technique: Determine the appropriate factoring technique for $4d^2 - 1$ . Since we have a difference of squares, we can use the formula $a^2 - b^2 = (a - b)(a + b)$ .
Identify terms as squares: Identify the terms in the expression $4d^2 - 1$ as squares. $\newline$ $4d^2$ can be written as $(2d)^2$ because $2d \times 2d = 4d^2$ . $\newline$ $1$ can be written as $1^2$ because $1 \times 1 = 1$ . $\newline$ So, $4d^2 - 1$ is in the form of $a^2 - b^2$ where $a = 2d$ and $4d^2$ $0$ .
Apply difference of squares formula: Apply the difference of squares formula to factor the expression. $\newline$ Using $a^2 - b^2 = (a - b)(a + b)$ , we get: $\newline$ $(2d)^2 - 1^2 = (2d - 1)(2d + 1)$ .
Write final factored form: Write the final factored form of the expression. $\newline$ The factored form of $4d^2 - 1$ is $(2d - 1)(2d + 1)$ .