Factor. 16w^2 - 25 ______

Identify factoring technique: Determine the appropriate factoring technique for 16w^2 - 25. Since we have a subtraction of two squares, we can use the difference of squares formula, which is a^2 - b^2 = (a - b)(a + b).Recognize as difference of squares: Recognize 16w^2 - 25 as a difference of squares. 16w^2 can be written as (4w)^2 because 4w * 4w = 16w^2. 25 can be written as 5^2 because 5 * 5 = 25. So, 16w^2 - 25 is in the form of a^2 - b^2 where a = 4w and b = 5.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 substitute a with 4w and b with 5. (4w)^2 - 5^2 = (4w - 5)(4w + 5)Write final factored form: Write the final factored form of the expression. The factored form of 16w^2 - 25 is (4w - 5)(4w + 5).

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Algebra 1

Factor quadratics: special cases

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Q. Factor.

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16w^2 - 25

Identify factoring technique: Determine the appropriate factoring technique for $16w^2 - 25$ . Since we have a subtraction of two squares, we can use the difference of squares formula, which is $a^2 - b^2 = (a - b)(a + b)$ .
Recognize as difference of squares: Recognize $16w^2 - 25$ as a difference of squares. $\newline$ $16w^2$ can be written as $(4w)^2$ because $4w \times 4w = 16w^2$ . $\newline$ $25$ can be written as $5^2$ because $5 \times 5 = 25$ . $\newline$ So, $16w^2 - 25$ is in the form of $a^2 - b^2$ where $a = 4w$ and $16w^2$ $0$ .
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 substitute $a$ with $4w$ and $b$ with $5$ . $\newline$ $(4w)^2 - 5^2 = (4w - 5)(4w + 5)$
Write final factored form: Write the final factored form of the expression. $\newline$ The factored form of $16w^2 - 25$ is $(4w - 5)(4w + 5)$ .