Factor. 25m^2 - 4 ______

Determine technique: Determine the appropriate factoring technique for 25m^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 terms: Identify the terms in the expression 25m^2 - 4 as squares. 25m^2 can be written as (5m)^2 because 5m * 5m = 25m^2. 4 can be written as 2^2 because 2 * 2 = 4. So, 25m^2 - 4 is in the form of a^2 - b^2 where a = 5m and b = 2.Apply 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 5m and b with 2. (5m)^2 - 2^2 = (5m + 2)(5m - 2)Write factored form: Write the final factored form of the expression. The factored form of 25m^2 - 4 is (5m + 2)(5m - 2).

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Algebra 1

Factor quadratics: special cases

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Q. Factor.

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25m^2 - 4

Determine technique: Determine the appropriate factoring technique for $25m^2 - 4$ . 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 terms: Identify the terms in the expression $25m^2 - 4$ as squares. $\newline$ $25m^2$ can be written as $(5m)^2$ because $5m \times 5m = 25m^2$ . $\newline$ $4$ can be written as $2^2$ because $2 \times 2 = 4$ . $\newline$ So, $25m^2 - 4$ is in the form of $a^2 - b^2$ where $a = 5m$ and $25m^2$ $0$ .
Apply 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 $5m$ and $b$ with $2$ . $\newline$ $(5m)^2 - 2^2 = (5m + 2)(5m - 2)$
Write factored form: Write the final factored form of the expression. $\newline$ The factored form of $25m^2 - 4$ is $(5m + 2)(5m - 2)$ .