Factor. 25z^2 - 1 ______

Recognize difference of squares: Determine the approach to factor 25z^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 terms in expression: Identify 25z^2 - 1 in the form of a^2 - b^2. 25z^2 can be written as (5z)^2 because 5z * 5z = 25z^2. 1 can be written as 1^2 because 1 * 1 = 1. So, 25z^2 - 1 = (5z)^2 - 1^2.Apply formula to factor: Apply the difference of squares formula to factor the expression. Using the formula a^2 - b^2 = (a - b)(a + b), we get: (5z)^2 - 1^2 = (5z - 1)(5z + 1).

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Math Problems

Algebra 1

Factor quadratics: special cases

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Q. Factor.

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25z^2 - 1

Recognize difference of squares: Determine the approach to factor $25z^2 - 1$ . 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 terms in expression: Identify $25z^2 - 1$ in the form of $a^2 - b^2$ . $\newline$ $25z^2$ can be written as $(5z)^2$ because $5z \times 5z = 25z^2$ . $\newline$ $1$ can be written as $1^2$ because $1 \times 1 = 1$ . $\newline$ So, $25z^2 - 1 = (5z)^2 - 1^2$ .
Apply formula to factor: Apply the difference of squares formula to factor the expression. $\newline$ Using the formula $a^2 - b^2 = (a - b)(a + b)$ , we get: $\newline$ $(5z)^2 - 1^2 = (5z - 1)(5z + 1)$ .