Factor. 16z^2 - 1 ______

Determine Factoring Technique: Determine the appropriate factoring technique for 16z^2 - 1. Since we have a difference of squares, we can use the identity (a^2 - b^2) = (a - b)(a + b).Identify Perfect Squares: Identify the terms in the expression 16z^2 - 1 as perfect squares. 16z^2 can be written as (4z)^2 because 4z * 4z = 16z^2. 1 can be written as 1^2 because 1 * 1 = 1. So, 16z^2 - 1 is in the form of a^2 - b^2 where a = 4z 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 substitute a with 4z and b with 1. (4z)^2 - 1^2 = (4z - 1)(4z + 1)Write Factored Form: Write down the factored form of the expression. The factored form of 16z^2 - 1 is (4z - 1)(4z + 1).

Home

Math Problems

Algebra 1

Factor quadratics: special cases

Full solution

Q. Factor.

\newline

16z^2 - 1

Determine Factoring Technique: Determine the appropriate factoring technique for $16z^2 - 1$ . Since we have a difference of squares, we can use the identity $(a^2 - b^2) = (a - b)(a + b)$ .
Identify Perfect Squares: Identify the terms in the expression $16z^2 - 1$ as perfect squares. $\newline$ $16z^2$ can be written as $(4z)^2$ because $4z \times 4z = 16z^2$ . $\newline$ $1$ can be written as $1^2$ because $1 \times 1 = 1$ . $\newline$ So, $16z^2 - 1$ is in the form of $a^2 - b^2$ where $a = 4z$ and $16z^2$ $0$ .
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 substitute $a$ with $4z$ and $b$ with $1$ . $\newline$ $(4z)^2 - 1^2 = (4z - 1)(4z + 1)$
Write Factored Form: Write down the factored form of the expression. $\newline$ The factored form of $16z^2 - 1$ is $(4z - 1)(4z + 1)$ .