Factor. 16k^2 - 25 ______

Determine approach: Determine the approach to factor 16k^2 - 25. We can observe that the expression is a difference of squares, which can be factored using the formula a^2 - b^2 = (a - b)(a + b).Identify expression form: Identify 16k^2 - 25 in the form of a^2 - b^2. 16k^2 can be written as (4k)^2 because 4k * 4k = 16k^2. 25 can be written as 5^2 because 5 * 5 = 25. So, 16k^2 - 25 is in the form (4k)^2 - 5^2.Apply formula to factor: 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 4k and b with 5. (4k)^2 - 5^2 = (4k - 5)(4k + 5).

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Algebra 1

Factor quadratics: special cases

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Q. Factor.

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16k^2 - 25

Determine approach: Determine the approach to factor $16k^2 - 25$ . We can observe that the expression is a difference of squares, which can be factored using the formula $a^2 - b^2 = (a - b)(a + b)$ .
Identify expression form: Identify $16k^2 - 25$ in the form of $a^2 - b^2$ .
$16k^2$ can be written as $(4k)^2$ because $4k \times 4k = 16k^2$ .
$25$ can be written as $5^2$ because $5 \times 5 = 25$ .
So, $16k^2 - 25$ is in the form $(4k)^2 - 5^2$ .
Apply formula to factor: 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 $4k$ and $b$ with $5$ . $(4k)^2 - 5^2 = (4k - 5)(4k + 5)$ .