Factor. 16t^2 - 25 ______

Approach Determination: Determine the approach to factor 16t^2 - 25. We can observe that 16t^2 and 25 are both perfect squares, and they are being subtracted from each other. This suggests that we can use the difference of squares formula, which is a^2 - b^2 = (a - b)(a + b).Identify Form: Identify 16t^2 - 25 in the form of a^2 - b^2. 16t^2 can be written as (4t)^2 because 4t * 4t = 16t^2. 25 can be written as 5^2 because 5 * 5 = 25. So, 16t^2 - 25 can be rewritten as (4t)^2 - 5^2.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 4t and b with 5. (4t)^2 - 5^2 = (4t - 5)(4t + 5).Final Factored Form: Write the final factored form. The factored form of 16t^2 - 25 is (4t - 5)(4t + 5).

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Algebra 1

Factor quadratics: special cases

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Q. Factor.

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16t^2 - 25

Approach Determination: Determine the approach to factor $16t^2 - 25$ . We can observe that $16t^2$ and $25$ are both perfect squares, and they are being subtracted from each other. This suggests that we can use the difference of squares formula, which is $a^2 - b^2 = (a - b)(a + b)$ .
Identify Form: Identify $16t^2 - 25$ in the form of $a^2 - b^2$ . $\newline$ $16t^2$ can be written as $(4t)^2$ because $4t \times 4t = 16t^2$ . $\newline$ $25$ can be written as $5^2$ because $5 \times 5 = 25$ . $\newline$ So, $16t^2 - 25$ can be rewritten as $(4t)^2 - 5^2$ .
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 $4t$ and $b$ with $5$ . $\newline$ $(4t)^2 - 5^2 = (4t - 5)(4t + 5)$ .
Final Factored Form: Write the final factored form. $\newline$ The factored form of $16t^2 - 25$ is $(4t - 5)(4t + 5)$ .