Factor. 16m^2 - 9 ______

Approach Determination: Determine the approach to factor 16m^2 - 9. We can observe that 16m^2 and 9 are both perfect squares, and they are being subtracted from each other. This suggests that we can use the difference of squares method to factor the expression. The difference of squares formula is a^2 - b^2 = (a - b)(a + b).Identify Form: Identify 16m^2 - 9 in the form of a^2 - b^2. 16m^2 can be written as (4m)^2 because 4m * 4m = 16m^2. 9 can be written as 3^2 because 3 * 3 = 9. So, 16m^2 - 9 can be rewritten as (4m)^2 - 3^2.Apply Formula: Apply the difference of squares formula to factor the expression. Using the formula a^2 - b^2 = (a - b)(a + b), we substitute a with 4m and b with 3. (4m)^2 - 3^2 = (4m - 3)(4m + 3).Write Factored Form: Write the final factored form of the expression. The factored form of 16m^2 - 9 is (4m - 3)(4m + 3).

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Algebra 1

Factor quadratics: special cases

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Q. Factor.

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16m^2 - 9

Approach Determination: Determine the approach to factor $16m^2 - 9$ . We can observe that $16m^2$ and $9$ are both perfect squares, and they are being subtracted from each other. This suggests that we can use the difference of squares method to factor the expression. The difference of squares formula is $a^2 - b^2 = (a - b)(a + b)$ .
Identify Form: Identify $16m^2 - 9$ in the form of $a^2 - b^2$ . $\newline$ $16m^2$ can be written as $(4m)^2$ because $4m \times 4m = 16m^2$ . $\newline$ $9$ can be written as $3^2$ because $3 \times 3 = 9$ . $\newline$ So, $16m^2 - 9$ can be rewritten as $(4m)^2 - 3^2$ .
Apply Formula: Apply the difference of squares formula to factor the expression. $\newline$ Using the formula $a^2 - b^2 = (a - b)(a + b)$ , we substitute $a$ with $4m$ and $b$ with $3$ . $\newline$ $(4m)^2 - 3^2 = (4m - 3)(4m + 3)$ .
Write Factored Form: Write the final factored form of the expression. $\newline$ The factored form of $16m^2 - 9$ is $(4m - 3)(4m + 3)$ .