Factor completely. 27x^(2)-3 Answer:

Identify Form: Identify the form of the expression. The given expression is 27x^2 - 3, which is a difference of squares because it can be written as (3x)^2 - (sqrt(3))^2.Apply Formula: Apply the difference of squares formula. The difference of squares formula is a^2 - b^2 = (a + b)(a - b). Here, a = 3x and b = sqrt(3).Factor Expression: Factor the expression using the formula. Substitute a = 3x and b = sqrt(3) into the formula to get (3x + sqrt(3))(3x - sqrt(3)).Check Factoring: Check the factoring. (3x + sqrt(3))(3x - sqrt(3)) = (3x)^2 - (sqrt(3))^2 = 9x^2 - 3, which is not the original expression. We made a mistake in the calculation of (3x)^2. It should be 27x^2, not 9x^2. Therefore, there is a math error.

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Q. Factor completely.

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27 x^{2}-3

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Answer:

Identify Form: Identify the form of the expression. $\newline$ The given expression is $27x^2 - 3$ , which is a difference of squares because it can be written as $(3x)^2 - (\sqrt{3})^2$ .
Apply Formula: Apply the difference of squares formula. $\newline$ The difference of squares formula is $a^2 - b^2 = (a + b)(a - b)$ . Here, $a = 3x$ and $b = \sqrt{3}$ .
Factor Expression: Factor the expression using the formula. $\newline$ Substitute $a = 3x$ and $b = \sqrt{3}$ into the formula to get $(3x + \sqrt{3})(3x - \sqrt{3})$ .
Check Factoring: Check the factoring. $\newline$ $(3x + \sqrt{3})(3x - \sqrt{3}) = (3x)^2 - (\sqrt{3})^2 = 9x^2 - 3$ , which is not the original expression. We made a mistake in the calculation of $(3x)^2$ . It should be $27x^2$ , not $9x^2$ . Therefore, there is a math error.