Factor. 25v^2 - 4 ______

Determine Factoring Technique: Determine the appropriate factoring technique for 25v^2 - 4. 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 25v^2 - 4 as perfect squares. 25v^2 can be written as (5v)^2 because 5v * 5v = 25v^2. 4 can be written as 2^2 because 2 * 2 = 4. So, 25v^2 - 4 is in the form of a^2 - b^2 where a = 5v and b = 2.Apply Difference of Squares Formula: Apply the difference of squares formula to factor the expression. Using a = 5v and b = 2, we get: 25v^2 - 4 = (5v)^2 - 2^2 = (5v - 2)(5v + 2).Write Final Factored Form: Write down the final factored form of the expression. The factored form of 25v^2 - 4 is (5v - 2)(5v + 2).

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Math Problems

Algebra 1

Factor quadratics: special cases

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Q. Factor.

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25v^2 - 4

Determine Factoring Technique: Determine the appropriate factoring technique for $25v^2 - 4$ . 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 $25v^2 - 4$ as perfect squares. $25v^2$ can be written as $(5v)^2$ because $5v \times 5v = 25v^2$ . $4$ can be written as $2^2$ because $2 \times 2 = 4$ .So, $25v^2 - 4$ is in the form of $a^2 - b^2$ where $a = 5v$ and $25v^2$ $0$ .
Apply Difference of Squares Formula: Apply the difference of squares formula to factor the expression. $\newline$ Using $a = 5v$ and $b = 2$ , we get: $\newline$ $25v^2 - 4 = (5v)^2 - 2^2 = (5v - 2)(5v + 2)$ .
Write Final Factored Form: Write down the final factored form of the expression. $\newline$ The factored form of $25v^2 - 4$ is $(5v - 2)(5v + 2)$ .