Factor. 16t^2 - 1 ______

Identify Factoring Technique: Determine the appropriate factoring technique for 16t^2 - 1. Since we have a difference of squares, we can use the identity (a^2 - b^2) = (a - b)(a + b).Identify Squares in Expression: Identify the terms in the expression 16t^2 - 1 as squares. 16t^2 can be written as (4t)^2 because 4t * 4t = 16t^2. 1 can be written as 1^2 because 1 * 1 = 1. So, 16t^2 - 1 is in the form of a^2 - b^2 where a = 4t and b = 1.Apply Difference of Squares Formula: Apply the difference of squares formula to factor the expression. Using the identity (a^2 - b^2) = (a - b)(a + b), we get: (4t)^2 - 1^2 = (4t - 1)(4t + 1).

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Math Problems

Algebra 1

Factor quadratics: special cases

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Q. Factor.

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16t^2 - 1

Identify Factoring Technique: Determine the appropriate factoring technique for $16t^2 - 1$ . $\newline$ Since we have a difference of squares, we can use the identity $(a^2 - b^2) = (a - b)(a + b)$ .
Identify Squares in Expression: Identify the terms in the expression $16t^2 - 1$ as squares. $\newline$ $16t^2$ can be written as $(4t)^2$ because $4t \times 4t = 16t^2$ . $\newline$ $1$ can be written as $1^2$ because $1 \times 1 = 1$ . $\newline$ So, $16t^2 - 1$ is in the form of $a^2 - b^2$ where $a = 4t$ and $16t^2$ $0$ .
Apply Difference of Squares Formula: Apply the difference of squares formula to factor the expression. $\newline$ Using the identity $(a^2 - b^2) = (a - b)(a + b)$ , we get: $\newline$ $(4t)^2 - 1^2 = (4t - 1)(4t + 1)$ .