Factor. 4g^2 - 9 ______

Identify Factoring Type: Identify the type of factoring required for 4g^2 - 9. This expression is a difference of squares because it can be written as a^2 - b^2, where a^2 = 4g^2 and b^2 = 9.Rewrite as Squares: Rewrite 4g^2 and 9 as squares. 4g^2 can be written as (2g)^2 because 2g * 2g = 4g^2. 9 can be written as 3^2 because 3 * 3 = 9. So, 4g^2 - 9 can be rewritten as (2g)^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 can factor (2g)^2 - 3^2 as (2g - 3)(2g + 3).

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Algebra 1

Factor quadratics: special cases

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Q. Factor.

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4g^2 - 9

Identify Factoring Type: Identify the type of factoring required for $4g^2 - 9$ . This expression is a difference of squares because it can be written as $a^2 - b^2$ , where $a^2 = 4g^2$ and $b^2 = 9$ .
Rewrite as Squares: Rewrite $4g^2$ and $9$ as squares. $\newline$ $4g^2$ can be written as $(2g)^2$ because $2g \times 2g = 4g^2$ . $\newline$ $9$ can be written as $3^2$ because $3 \times 3 = 9$ . $\newline$ So, $4g^2 - 9$ can be rewritten as $(2g)^2 - 3^2$ .
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 can factor $(2g)^2 - 3^2$ as $(2g - 3)(2g + 3)$ .