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Factor. $\newline$ $25r^2 - 16$

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Factor quadratics: special cases

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Q. Factor.

\newline

25r^2 - 16

Determine factoring technique: Determine the appropriate factoring technique for $25r^2 - 16$ . Since we have a difference of squares, we can use the formula $a^2 - b^2 = (a - b)(a + b)$ .
Identify perfect squares: Identify the terms in the expression $25r^2 - 16$ as perfect squares. $\newline$ $25r^2$ can be written as $(5r)^2$ because $5r \times 5r = 25r^2$ . $\newline$ $16$ can be written as $4^2$ because $4 \times 4 = 16$ . $\newline$ So, $25r^2 - 16$ is in the form of $a^2 - b^2$ where $a = 5r$ and $25r^2$ $0$ .
Apply difference of squares formula: Apply the difference of squares formula to factor the expression. $\newline$ Using $a = 5r$ and $b = 4$ , we get: $\newline$ $(5r)^2 - 4^2 = (5r - 4)(5r + 4)$ .
Write factored form: Write down the factored form of the expression. $\newline$ The factored form of $25r^2 - 16$ is $(5r - 4)(5r + 4)$ .

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