Factor. 25k^2 - 4 ______

Determine factoring technique: Determine the appropriate factoring technique for 25k^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 25k^2 - 4 as perfect squares. 25k^2 can be written as (5k)^2 because 5k * 5k = 25k^2. 4 can be written as 2^2 because 2 * 2 = 4. So, 25k^2 - 4 is in the form of a^2 - b^2 where a = 5k and b = 2.Apply difference of squares formula: Apply the difference of squares formula to factor the expression. Using a = 5k and b = 2, we get: 25k^2 - 4 = (5k)^2 - 2^2 = (5k - 2)(5k + 2).

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Math Problems

Algebra 1

Factor quadratics: special cases

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Q. Factor.

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25k^2 - 4

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