Factor. 25t^2 - 16 ______

Determine Approach: Determine the approach to factor 25t^2 - 16. 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 Perfect Squares: Identify 25t^2 and 16 as perfect squares. 25t^2 can be written as (5t)^2 because 5t * 5t = 25t^2. 16 can be written as 4^2 because 4 * 4 = 16. So, 25t^2 - 16 can be expressed as (5t)^2 - 4^2.Apply Formula: Apply the difference of squares formula to factor the expression. Using the formula a^2 - b^2 = (a - b)(a + b), we get: (5t)^2 - 4^2 = (5t - 4)(5t + 4).Write Final Form: Write the final factored form. The factored form of 25t^2 - 16 is (5t - 4)(5t + 4).

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Math Problems

Algebra 1

Factor quadratics: special cases

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Q. Factor.

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25t^2 - 16

Determine Approach: Determine the approach to factor $25t^2 - 16$ . 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 Perfect Squares: Identify $25t^2$ and $16$ as perfect squares. $\newline$ $25t^2$ can be written as $(5t)^2$ because $5t \times 5t = 25t^2$ . $\newline$ $16$ can be written as $4^2$ because $4 \times 4 = 16$ . $\newline$ So, $25t^2 - 16$ can be expressed as $(5t)^2 - 4^2$ .
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 get: $\newline$ $(5t)^2 - 4^2 = (5t - 4)(5t + 4)$ .
Write Final Form: Write the final factored form. $\newline$ The factored form of $25t^2 - 16$ is $(5t - 4)(5t + 4)$ .