Factor. 16r^2 - 1 ______

Determine Factoring Technique: Determine the appropriate factoring technique for 16r^2 - 1. Since we have a difference of squares, we can use the formula a^2 - b^2 = (a - b)(a + b).Identify Squares in Expression: Identify the terms in the expression 16r^2 - 1 as squares. 16r^2 can be written as (4r)^2 because 4r * 4r = 16r^2. 1 can be written as 1^2 because 1 * 1 = 1. So, 16r^2 - 1 is in the form of a^2 - b^2 where a = 4r and b = 1.Apply Difference of Squares Formula: Apply the difference of squares formula to factor the expression. Using a = 4r and b = 1, we get: (4r)^2 - 1^2 = (4r - 1)(4r + 1).Write Factored Form: Write down the factored form of the expression. The factored form of 16r^2 - 1 is (4r - 1)(4r + 1).

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Math Problems

Algebra 1

Factor quadratics: special cases

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Q. Factor.

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16r^2 - 1

Determine Factoring Technique: Determine the appropriate factoring technique for $16r^2 - 1$ . Since we have a difference of squares, we can use the formula $a^2 - b^2 = (a - b)(a + b)$ .
Identify Squares in Expression: Identify the terms in the expression $16r^2 - 1$ as squares. $\newline$ $16r^2$ can be written as $(4r)^2$ because $4r \times 4r = 16r^2$ . $\newline$ $1$ can be written as $1^2$ because $1 \times 1 = 1$ . $\newline$ So, $16r^2 - 1$ is in the form of $a^2 - b^2$ where $a = 4r$ and $16r^2$ $0$ .
Apply Difference of Squares Formula: Apply the difference of squares formula to factor the expression. $\newline$ Using $a = 4r$ and $b = 1$ , we get: $\newline$ $(4r)^2 - 1^2 = (4r - 1)(4r + 1)$ .
Write Factored Form: Write down the factored form of the expression. $\newline$ The factored form of $16r^2 - 1$ is $(4r - 1)(4r + 1)$ .