Factor. 16z^2 - 25 ______

Determine Factoring Technique: Determine the appropriate factoring technique for 16z^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).Identify Squares in Expression: Identify the terms in the expression 16z^2 - 25 as squares. 16z^2 can be written as (4z)^2 because 4z * 4z = 16z^2. 25 can be written as 5^2 because 5 * 5 = 25. So, 16z^2 - 25 can be rewritten as (4z)^2 - 5^2.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 substitute a with 4z and b with 5. (4z)^2 - 5^2 = (4z - 5)(4z + 5).

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Algebra 1

Factor quadratics: special cases

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Q. Factor.

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16z^2 - 25

Determine Factoring Technique: Determine the appropriate factoring technique for $16z^2 - 25$ . Since we have a subtraction of two squares, we can use the difference of squares formula, which is $a^2 - b^2 = (a - b)(a + b)$ .
Identify Squares in Expression: Identify the terms in the expression $16z^2 - 25$ as squares. $\newline$ $16z^2$ can be written as $(4z)^2$ because $4z \times 4z = 16z^2$ . $\newline$ $25$ can be written as $5^2$ because $5 \times 5 = 25$ . $\newline$ So, $16z^2 - 25$ can be rewritten as $(4z)^2 - 5^2$ .
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 substitute $a$ with $4z$ and $b$ with $5$ . $\newline$ $(4z)^2 - 5^2 = (4z - 5)(4z + 5)$ .