Factor. 16m^2 - 1 ______

Recognize Difference of Squares: Determine the appropriate method to factor 16m^2 - 1. We can recognize this expression as a difference of squares because it is in the form a^2 - b^2, where both terms are perfect squares.Identify Squares: Identify the squares in the expression 16m^2 - 1. 16m^2 can be written as (4m)^2 because 4m * 4m = 16m^2. 1 can be written as 1^2 because 1 * 1 = 1. So, 16m^2 - 1 is in the form (4m)^2 - 1^2.Apply Formula: Apply the difference of squares formula to factor the expression. The difference of squares formula is a^2 - b^2 = (a - b)(a + b). Using this formula, we can write (4m)^2 - 1^2 as (4m - 1)(4m + 1).Write Factored Form: Write the final factored form of the expression. The factored form of 16m^2 - 1 is (4m - 1)(4m + 1).

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Algebra 1

Factor quadratics: special cases

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Q. Factor.

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16m^2 - 1

Recognize Difference of Squares: Determine the appropriate method to factor $16m^2 - 1$ . We can recognize this expression as a difference of squares because it is in the form $a^2 - b^2$ , where both terms are perfect squares.
Identify Squares: Identify the squares in the expression $16m^2 - 1$ . $16m^2$ can be written as $(4m)^2$ because $4m \times 4m = 16m^2$ . $1$ can be written as $1^2$ because $1 \times 1 = 1$ . So, $16m^2 - 1$ is in the form $(4m)^2 - 1^2$ .
Apply Formula: Apply the difference of squares formula to factor the expression. $\newline$ The difference of squares formula is $a^2 - b^2 = (a - b)(a + b)$ . $\newline$ Using this formula, we can write $(4m)^2 - 1^2$ as $(4m - 1)(4m + 1)$ .
Write Factored Form: Write the final factored form of the expression. $\newline$ The factored form of $16m^2 - 1$ is $(4m - 1)(4m + 1)$ .