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

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Factor quadratics: special cases

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Q. Factor.

\newline

16f^2 - 25

Determine method for factoring: Determine the appropriate method to factor the expression $16f^2 - 25$ . The expression is a difference of squares, which can be factored using the formula $a^2 - b^2 = (a - b)(a + b)$ .
Identify perfect squares: Identify the terms in the expression $16f^2 - 25$ as perfect squares. $\newline$ $16f^2$ is a perfect square because $16$ is $4$ squared and $f^2$ is $f$ squared, so $(4f)^2$ . $\newline$ $25$ is a perfect square because it is $5$ squared, so $5^2$ . $\newline$ Therefore, $16f^2 - 25$ can be written as $16f^2$ $1$ .
Apply difference of squares 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 $4f$ and $b$ with $5$ . $\newline$ $(4f)^2 - 5^2 = (4f - 5)(4f + 5)$ .

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