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Factor. $\newline$ $4f^2 - 9$

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Factor quadratics: special cases

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Q. Factor.

\newline

4f^2 - 9

Determine factoring technique: Determine the appropriate factoring technique for $4f^2 - 9$ . Since we have a subtraction of two squares, we can use the difference of squares formula: $(a^2 - b^2) = (a + b)(a - b)$ .
Identify perfect squares: Identify the terms in the expression $4f^2 - 9$ as perfect squares. $\newline$ $4f^2$ can be written as $(2f)^2$ because $2f \times 2f = 4f^2$ . $\newline$ $9$ can be written as $3^2$ because $3 \times 3 = 9$ . $\newline$ So, $4f^2 - 9$ is in the form of $a^2 - b^2$ where $a = 2f$ and $4f^2$ $0$ .
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 get: $\newline$ $(2f)^2 - 3^2 = (2f + 3)(2f - 3)$ .
Write factored form: Write down the factored form of the expression. $\newline$ The factored form of $4f^2 - 9$ is $(2f + 3)(2f - 3)$ .

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