Factor. z^2 - 16 ______

Recognize difference of squares: Determine the appropriate method to factor z^2 - 16. We recognize that z^2 - 16 is a difference of squares because it can be written in the form a^2 - b^2, where a = z and b = 4 (since 4^2 = 16).Write expression in correct form: Write z^2 - 16 as a difference of squares. z^2 = z * z = (z)^2 16 = 4 * 4 = 4^2 Therefore, z^2 - 16 can be expressed as (z)^2 - 4^2.Apply difference of squares formula: Apply the difference of squares formula to factor the expression. The difference of squares formula is a^2 - b^2 = (a - b)(a + b). Using this formula, we get (z)^2 - 4^2 = (z - 4)(z + 4).Write final factored form: Write the final factored form of z^2 - 16. The factored form of z^2 - 16 is (z - 4)(z + 4).

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Algebra 1

Factor quadratics: special cases

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Q. Factor.

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z^2 - 16

Recognize difference of squares: Determine the appropriate method to factor $z^2 - 16$ . We recognize that $z^2 - 16$ is a difference of squares because it can be written in the form $a^2 - b^2$ , where $a = z$ and $b = 4$ (since $4^2 = 16$ ).
Write expression in correct form: Write $z^2 - 16$ as a difference of squares. $\newline$ $z^2 = z \times z = (z)^2$ $\newline$ $16 = 4 \times 4 = 4^2$ $\newline$ Therefore, $z^2 - 16$ can be expressed as $(z)^2 - 4^2$ .
Apply difference of squares formula: Apply the difference of squares formula to factor the expression. $\newline$ The difference of squares formula is $a^2 - b^2 = (a - b)(a + b)$ . $\newline$ Using this formula, we get $(z)^2 - 4^2 = (z - 4)(z + 4)$ .
Write final factored form: Write the final factored form of $z^2 - 16$ . The factored form of $z^2 - 16$ is $(z - 4)(z + 4)$ .