Factor. 25p^2 - 4 ______

Identify Technique: Determine the appropriate factoring technique for 25p^2 - 4. Since we have a difference of squares, we can use the identity (a^2 - b^2) = (a + b)(a - b).Identify Perfect Squares: Identify the terms in the expression 25p^2 - 4 as perfect squares. 25p^2 can be written as (5p)^2 because 5p * 5p = 25p^2. 4 can be written as 2^2 because 2 * 2 = 4. So, 25p^2 - 4 is in the form of a^2 - b^2 where a = 5p and b = 2.Apply Difference of Squares Formula: Apply the difference of squares formula to factor the expression. Using the identity (a^2 - b^2) = (a + b)(a - b), we substitute a = 5p and b = 2 to get: (5p)^2 - 2^2 = (5p + 2)(5p - 2).

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Math Problems

Algebra 1

Factor quadratics: special cases

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Q. Factor.

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25p^2 - 4

Identify Technique: Determine the appropriate factoring technique for $25p^2 - 4$ . Since we have a difference of squares, we can use the identity $(a^2 - b^2) = (a + b)(a - b)$ .
Identify Perfect Squares: Identify the terms in the expression $25p^2 - 4$ as perfect squares. $\newline$ $25p^2$ can be written as $(5p)^2$ because $5p \times 5p = 25p^2$ . $\newline$ $4$ can be written as $2^2$ because $2 \times 2 = 4$ . $\newline$ So, $25p^2 - 4$ is in the form of $a^2 - b^2$ where $a = 5p$ and $25p^2$ $0$ .
Apply Difference of Squares Formula: Apply the difference of squares formula to factor the expression. $\newline$ Using the identity $(a^2 - b^2) = (a + b)(a - b)$ , we substitute $a = 5p$ and $b = 2$ to get: $\newline$ $(5p)^2 - 2^2 = (5p + 2)(5p - 2)$ .