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

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Factor quadratics: special cases

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Q. Factor.

\newline

25u^2 - 4

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

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