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Factor. $\newline$ $25r^2 - 4$

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Factor quadratics: special cases

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Q. Factor.

\newline

25r^2 - 4

Determine Method: Determine the appropriate method to factor the expression $25r^2 - 4$ . This expression is a difference of squares because it can be written as $a^2 - b^2$ , where $a^2$ is a perfect square and $b^2$ is a perfect square.
Identify Squares: Identify the terms in the expression $25r^2 - 4$ as squares. $\newline$ $25r^2$ can be written as $(5r)^2$ because $5r \times 5r = 25r^2$ . $\newline$ $4$ can be written as $2^2$ because $2 \times 2 = 4$ . $\newline$ So, $25r^2 - 4$ is in the form of $a^2 - b^2$ where $a = 5r$ and $25r^2$ $0$ .
Apply Formula: Apply the difference of squares formula to factor the expression. $\newline$ The difference of squares formula is $a^2 - b^2 = (a - b)(a + b)$ . $\newline$ Using $a = 5r$ and $b = 2$ , we get: $\newline$ $(5r)^2 - 2^2 = (5r - 2)(5r + 2)$ .
Write Factored Form: Write the final factored form of the expression. $\newline$ The factored form of $25r^2 - 4$ is $(5r - 2)(5r + 2)$ .

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