Factor. 9c^2 - 1 ______

Determine factoring technique: Determine the appropriate factoring technique for 9c^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 9c^2 - 1 as perfect squares. 9c^2 can be written as (3c)^2 because 3c * 3c = 9c^2. 1 can be written as 1^2 because 1 * 1 = 1. So, 9c^2 - 1 is in the form of a^2 - b^2 where a = 3c 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: (3c)^2 - 1^2 = (3c + 1)(3c - 1).Write factored form: Write down the factored form of the expression. The factored form of 9c^2 - 1 is (3c + 1)(3c - 1).

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Math Problems

Algebra 1

Factor quadratics: special cases

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Q. Factor.

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9c^2 - 1

Determine factoring technique: Determine the appropriate factoring technique for $9c^2 - 1$ . 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 $9c^2 - 1$ as perfect squares. $\newline$ $9c^2$ can be written as $(3c)^2$ because $3c \times 3c = 9c^2$ . $\newline$ $1$ can be written as $1^2$ because $1 \times 1 = 1$ . $\newline$ So, $9c^2 - 1$ is in the form of $a^2 - b^2$ where $a = 3c$ and $9c^2$ $0$ .
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: $\newline$ $(3c)^2 - 1^2 = (3c + 1)(3c - 1)$ .
Write factored form: Write down the factored form of the expression. $\newline$ The factored form of $9c^2 - 1$ is $(3c + 1)(3c - 1)$ .