Factor. 16p^2 - 1 ______

Recognize Factoring Pattern: Determine if the expression fits a known factoring pattern. The expression 16p^2 - 1 resembles the difference of squares pattern, which is a^2 - b^2 = (a - b)(a + b).Identify Squares: Identify the terms in the expression as squares. 16p^2 can be written as (4p)^2 because 4p * 4p = 16p^2. 1 can be written as 1^2 because 1 * 1 = 1. So, 16p^2 - 1 can be rewritten as (4p)^2 - 1^2.Apply Difference of Squares Formula: Apply the difference of squares formula to factor the expression. Using the formula a^2 - b^2 = (a - b)(a + b), we can factor the expression as follows: (4p)^2 - 1^2 = (4p - 1)(4p + 1).

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Math Problems

Algebra 1

Factor quadratics: special cases

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Q. Factor.

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16p^2 - 1

Recognize Factoring Pattern: Determine if the expression fits a known factoring pattern. $\newline$ The expression $16p^2 - 1$ resembles the difference of squares pattern, which is $a^2 - b^2 = (a - b)(a + b)$ .
Identify Squares: Identify the terms in the expression as squares. $\newline$ $16p^2$ can be written as $(4p)^2$ because $4p \times 4p = 16p^2$ . $\newline$ $1$ can be written as $1^2$ because $1 \times 1 = 1$ . $\newline$ So, $16p^2 - 1$ can be rewritten as $(4p)^2 - 1^2$ .
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 can factor the expression as follows: $\newline$ $(4p)^2 - 1^2 = (4p - 1)(4p + 1)$ .