Factor. q^2 - 9 ______

Identify Technique: Determine the appropriate factoring technique for q^2 - 9. Since we have a difference of squares, we can use the identity (a^2 - b^2) = (a + b)(a - b).Identify Expression: Identify q^2 - 9 as a difference of squares. q^2 can be written as (q)^2, and 9 can be written as 3^2, which means q^2 - 9 is in the form of a^2 - b^2 where a = q and b = 3.Apply Formula: Apply the difference of squares formula to factor q^2 - 9. Using the identity (a^2 - b^2) = (a + b)(a - b), we get (q + 3)(q - 3).Write Final Form: Write down the final factored form. The factored form of q^2 - 9 is (q + 3)(q - 3).

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Math Problems

Algebra 1

Factor quadratics: special cases

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Q. Factor.

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q^2 - 9

Identify Technique: Determine the appropriate factoring technique for $q^2 - 9$ . Since we have a difference of squares, we can use the identity $(a^2 - b^2) = (a + b)(a - b)$ .
Identify Expression: Identify $q^2 - 9$ as a difference of squares. $\newline$ $q^2$ can be written as $(q)^2$ , and $9$ can be written as $3^2$ , which means $q^2 - 9$ is in the form of $a^2 - b^2$ where $a = q$ and $b = 3$ .
Apply Formula: Apply the difference of squares formula to factor $q^2 - 9$ . Using the identity $(a^2 - b^2) = (a + b)(a - b)$ , we get $(q + 3)(q - 3)$ .
Write Final Form: Write down the final factored form. $\newline$ The factored form of $q^2 - 9$ is $(q + 3)(q - 3)$ .