Factor. 4y^2 - 9 ______

Determine factoring technique: Determine the appropriate factoring technique for 4y^2 - 9. Since we have a subtraction of two squares, we can use the difference of squares formula, which is a^2 - b^2 = (a - b)(a + b).Identify terms as squares: Identify the terms in the expression 4y^2 - 9 as squares. 4y^2 can be written as (2y)^2 because 2y * 2y = 4y^2. 9 can be written as 3^2 because 3 * 3 = 9. So, 4y^2 - 9 can be rewritten as (2y)^2 - 3^2.Apply difference of squares formula: 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 2y and b with 3. (2y)^2 - 3^2 = (2y - 3)(2y + 3).

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Algebra 1

Factor quadratics: special cases

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Q. Factor.

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4y^2 - 9

Determine factoring technique: Determine the appropriate factoring technique for $4y^2 - 9$ . Since we have a subtraction of two squares, we can use the difference of squares formula, which is $a^2 - b^2 = (a - b)(a + b)$ .
Identify terms as squares: Identify the terms in the expression $4y^2 - 9$ as squares. $\newline$ $4y^2$ can be written as $(2y)^2$ because $2y \times 2y = 4y^2$ . $\newline$ $9$ can be written as $3^2$ because $3 \times 3 = 9$ . $\newline$ So, $4y^2 - 9$ can be rewritten as $(2y)^2 - 3^2$ .
Apply difference of squares formula: 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 $2y$ and $b$ with $3$ . $\newline$ $(2y)^2 - 3^2 = (2y - 3)(2y + 3)$ .