Factor completely. 25x^(2)-9 Answer:

Approach Determination: Determine the approach to factor 25x^2 - 9. This expression is a difference of squares because it can be written as a^2 - b^2, where a^2 is a perfect square and b^2 is a perfect square.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.Expression Factoring: Factor the expression using the difference of squares formula. The difference of squares formula is a^2 - b^2 = (a - b)(a + b). Applying this formula to our expression, we get: (5x)^2 - 3^2 = (5x - 3)(5x + 3).

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Math Problems

Algebra 1

Factor quadratics: special cases

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Q. Factor completely.

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25 x^{2}-9

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Answer:

Approach Determination: Determine the approach to factor $25x^2 - 9$ . This expression is a difference of squares because it can be written as $a^2 - b^2$ , where $a^2$ is a perfect square and $b^2$ is a perfect square.
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 $(5x)^2 - 3^2$ .
Expression Factoring: Factor the expression using the difference of squares formula. $\newline$ The difference of squares formula is $a^2 - b^2 = (a - b)(a + b)$ . $\newline$ Applying this formula to our expression, we get: $\newline$ $(5x)^2 - 3^2 = (5x - 3)(5x + 3)$ .