Factor. 25x^2 - 9 ______

Approach Determination: Determine the approach to factor 25x^2 - 9. We can observe that 25x^2 and 9 are both perfect squares, and they are being subtracted from each other. This suggests that we can use the difference of squares formula, which is a^2 - b^2 = (a - b)(a + b).Form Identification: Identify 25x^2 - 9 in the form of a^2 - b^2. 25x^2 can be written as (5x)^2 because 5x * 5x = 25x^2. 9 can be written as 3^2 because 3 * 3 = 9. So, 25x^2 - 9 can be rewritten as (5x)^2 - 3^2.Formula Application: Apply the difference of squares formula to factor the expression. Using the formula a^2 - b^2 = (a - b)(a + b), we substitute a with 5x and b with 3. (5x)^2 - 3^2 = (5x - 3)(5x + 3).Final Factored Form: Write the final factored form. The factored form of 25x^2 - 9 is (5x - 3)(5x + 3).

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Algebra 1

Factor quadratics: special cases

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Q. Factor.

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25x^2 - 9

Approach Determination: Determine the approach to factor $25x^2 - 9$ . We can observe that $25x^2$ and $9$ are both perfect squares, and they are being subtracted from each other. This suggests that we can use the difference of squares formula, which is $a^2 - b^2 = (a - b)(a + b)$ .
Form Identification: Identify $25x^2 - 9$ in the form of $a^2 - b^2$ .
$25x^2$ can be written as $(5x)^2$ because $5x \times 5x = 25x^2$ .
$9$ can be written as $3^2$ because $3 \times 3 = 9$ .
So, $25x^2 - 9$ can be rewritten as $(5x)^2 - 3^2$ .
Formula Application: Apply the difference of squares formula to factor the expression. $\newline$ Using the formula $a^2 - b^2 = (a - b)(a + b)$ , we substitute $a$ with $5x$ and $b$ with $3$ . $\newline$ $(5x)^2 - 3^2 = (5x - 3)(5x + 3)$ .
Final Factored Form: Write the final factored form. $\newline$ The factored form of $25x^2 - 9$ is $(5x - 3)(5x + 3)$ .