Factor completely. 49x^(2)-9=

Determine factoring technique: Determine the appropriate factoring technique for 49x^2 - 9. The 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.Identify terms in form: Identify the terms in the form of a^2 - b^2. 49x^2 can be written as (7x)^2 because 7x * 7x = 49x^2. 9 can be written as 3^2 because 3 * 3 = 9. So, 49x^2 - 9 can be rewritten as (7x)^2 - 3^2.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). Using this formula, we get (7x)^2 - 3^2 = (7x - 3)(7x + 3).

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Math Problems

Algebra 1

Factor quadratics: special cases

Full solution

Q. Factor completely.

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49x^{2}-9

Determine factoring technique: Determine the appropriate factoring technique for $49x^2 - 9$ . $\newline$ The 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.
Identify terms in form: Identify the terms in the form of $a^2 - b^2$ . $\newline$ $49x^2$ can be written as $(7x)^2$ because $7x \times 7x = 49x^2$ . $\newline$ $9$ can be written as $3^2$ because $3 \times 3 = 9$ . $\newline$ So, $49x^2 - 9$ can be rewritten as $(7x)^2 - 3^2$ .
Apply difference of squares formula: Apply the difference of squares formula to factor the expression. $\newline$ The difference of squares formula is $a^2 - b^2 = (a - b)(a + b)$ . $\newline$ Using this formula, we get $(7x)^2 - 3^2 = (7x - 3)(7x + 3)$ .