Factor. 9c^2 - 25 ______

Determine factoring technique: Determine the appropriate factoring technique for 9c^2 - 25. Since we have a difference of squares, we can use the formula a^2 - b^2 = (a - b)(a + b).Identify perfect squares: Identify the terms in the expression 9c^2 - 25 as perfect squares. 9c^2 can be written as (3c)^2 because 3c * 3c = 9c^2. 25 can be written as 5^2 because 5 * 5 = 25. So, 9c^2 - 25 is in the form of a^2 - b^2 where a = 3c and b = 5.Apply difference of squares formula: Apply the difference of squares formula to factor the expression. Using a = 3c and b = 5, we get: (3c)^2 - 5^2 = (3c - 5)(3c + 5).Write final factored form: Write the final factored form of the expression. The factored form of 9c^2 - 25 is (3c - 5)(3c + 5).

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Math Problems

Algebra 1

Factor quadratics: special cases

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Q. Factor.

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9c^2 - 25

Determine factoring technique: Determine the appropriate factoring technique for $9c^2 - 25$ . Since we have a difference of squares, we can use the formula $a^2 - b^2 = (a - b)(a + b)$ .
Identify perfect squares: Identify the terms in the expression $9c^2 - 25$ as perfect squares. $\newline$ $9c^2$ can be written as $(3c)^2$ because $3c \times 3c = 9c^2$ . $\newline$ $25$ can be written as $5^2$ because $5 \times 5 = 25$ . $\newline$ So, $9c^2 - 25$ 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 $a = 3c$ and $b = 5$ , we get: $\newline$ $(3c)^2 - 5^2 = (3c - 5)(3c + 5)$ .
Write final factored form: Write the final factored form of the expression. $\newline$ The factored form of $9c^2 - 25$ is $(3c - 5)(3c + 5)$ .