Factor. 25d^2 - 1 ______

Recognize difference of squares: Determine the approach to factor 25d^2 - 1. We recognize this expression as a difference of squares, which can be factored using the formula a^2 - b^2 = (a - b)(a + b).Identify in correct form: Identify 25d^2 - 1 in the form of a^2 - b^2. 25d^2 can be written as (5d)^2 because 5d * 5d = 25d^2. 1 can be written as 1^2 because 1 * 1 = 1. So, 25d^2 - 1 = (5d)^2 - 1^2.Apply formula for factoring: Apply the difference of squares formula to factor the expression. Using the formula a^2 - b^2 = (a - b)(a + b), we get: (5d)^2 - 1^2 = (5d - 1)(5d + 1).Write final factored form: Write the final factored form. The factored form of 25d^2 - 1 is (5d - 1)(5d + 1).

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Algebra 1

Factor quadratics: special cases

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Q. Factor.

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25d^2 - 1

Recognize difference of squares: Determine the approach to factor $25d^2 - 1$ . We recognize this expression as a difference of squares, which can be factored using the formula $a^2 - b^2 = (a - b)(a + b)$ .
Identify in correct form: Identify $25d^2 - 1$ in the form of $a^2 - b^2$ .
$25d^2$ can be written as $(5d)^2$ because $5d \times 5d = 25d^2$ .
$1$ can be written as $1^2$ because $1 \times 1 = 1$ .
So, $25d^2 - 1 = (5d)^2 - 1^2$ .
Apply formula for factoring: Apply the difference of squares formula to factor the expression. $\newline$ Using the formula $a^2 - b^2 = (a - b)(a + b)$ , we get: $\newline$ $(5d)^2 - 1^2 = (5d - 1)(5d + 1)$ .
Write final factored form: Write the final factored form. $\newline$ The factored form of $25d^2 - 1$ is $(5d - 1)(5d + 1)$ .