Factor. 9j^2 - 25 ______

Identify Perfect Squares: Determine if the expression 9j^2 - 25 can be factored using the difference of squares method. The difference of squares method is applicable when an expression is in the form a^2 - b^2, where both a and b are perfect squares. 9j^2 is a perfect square because it can be written as (3j)^2. 25 is a perfect square because it can be written as 5^2. Therefore, 9j^2 - 25 can be written as (3j)^2 - 5^2, which is in the form a^2 - b^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). Here, a = 3j and b = 5. Using the formula, we get (3j - 5)(3j + 5) as the factored form of 9j^2 - 25.

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Algebra 1

Factor quadratics: special cases

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Q. Factor.

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9j^2 - 25

Identify Perfect Squares: Determine if the expression $9j^2 - 25$ can be factored using the difference of squares method. $\newline$ The difference of squares method is applicable when an expression is in the form $a^2 - b^2$ , where both $a$ and $b$ are perfect squares. $\newline$ $9j^2$ is a perfect square because it can be written as $(3j)^2$ . $\newline$ $25$ is a perfect square because it can be written as $5^2$ . $\newline$ Therefore, $9j^2 - 25$ can be written as $(3j)^2 - 5^2$ , which is in the form $a^2 - b^2$ .
Apply Difference of Squares Formula: Apply the difference of squares formula to factor the expression. $\newline$ The difference of squares formula is $a^2 - b^2 = (a - b)(a + b)$ . $\newline$ Here, $a = 3j$ and $b = 5$ . $\newline$ Using the formula, we get $(3j - 5)(3j + 5)$ as the factored form of $9j^2 - 25$ .