Factor completely. 4x^(2)-1=

Determine factoring technique: Determine the appropriate factoring technique for 4x^2 - 1. Since we have a difference of squares, we can use the identity a^2 - b^2 = (a - b)(a + b).Identify terms as squares: Identify the terms in the expression 4x^2 - 1 as squares. 4x^2 can be written as (2x)^2 and 1 can be written as 1^2. So, 4x^2 - 1 = (2x)^2 - 1^2.Apply difference of squares formula: Apply the difference of squares formula to factor the expression. Using the identity from Step 1, we have: (2x)^2 - 1^2 = (2x - 1)(2x + 1).Verify no common factors: Verify that there are no common factors and that the expression cannot be factored further. The terms 2x - 1 and 2x + 1 have no common factors and cannot be factored further.

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Math Problems

Algebra 1

Factor quadratics: special cases

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Q. Factor completely.

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4x^{2}-1=

Determine factoring technique: Determine the appropriate factoring technique for $4x^2 - 1$ . $\newline$ Since we have a difference of squares, we can use the identity $a^2 - b^2 = (a - b)(a + b)$ .
Identify terms as squares: Identify the terms in the expression $4x^2 - 1$ as squares. $\newline$ $4x^2$ can be written as $(2x)^2$ and $1$ can be written as $1^2$ . $\newline$ So, $4x^2 - 1 = (2x)^2 - 1^2$ .
Apply difference of squares formula: Apply the difference of squares formula to factor the expression. $\newline$ Using the identity from Step $1$ , we have: $\newline$ $(2x)^2 - 1^2 = (2x - 1)(2x + 1)$ .
Verify no common factors: Verify that there are no common factors and that the expression cannot be factored further. $\newline$ The terms $2x - 1$ and $2x + 1$ have no common factors and cannot be factored further.