Factor. 4q^2 - 1 ______

Determine Factoring Technique: Determine the appropriate factoring technique for 4q^2 - 1. Since we have a difference of squares, we can use the identity a^2 - b^2 = (a - b)(a + b).Identify Squares in Expression: Identify the terms in the expression 4q^2 - 1 as squares. 4q^2 can be written as (2q)^2 because 2q * 2q = 4q^2. 1 can be written as 1^2 because 1 * 1 = 1. So, 4q^2 - 1 is in the form of a^2 - b^2 where a = 2q and b = 1.Apply Difference of Squares Formula: Apply the difference of squares formula to factor the expression. Using the identity from Step 1, we have: (2q)^2 - 1^2 = (2q - 1)(2q + 1).Write Factored Form: Write down the factored form of the expression. The factored form of 4q^2 - 1 is (2q - 1)(2q + 1).

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Math Problems

Algebra 1

Factor quadratics: special cases

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Q. Factor.

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4q^2 - 1

Determine Factoring Technique: Determine the appropriate factoring technique for $4q^2 - 1$ . Since we have a difference of squares, we can use the identity $a^2 - b^2 = (a - b)(a + b)$ .
Identify Squares in Expression: Identify the terms in the expression $4q^2 - 1$ as squares. $\newline$ $4q^2$ can be written as $(2q)^2$ because $2q \times 2q = 4q^2$ . $\newline$ $1$ can be written as $1^2$ because $1 \times 1 = 1$ . $\newline$ So, $4q^2 - 1$ is in the form of $a^2 - b^2$ where $a = 2q$ and $4q^2$ $0$ .
Apply Difference of Squares Formula: Apply the difference of squares formula to factor the expression. $\newline$ Using the identity from Step $1$ , we have: $\newline$ $(2q)^2 - 1^2 = (2q - 1)(2q + 1)$ .
Write Factored Form: Write down the factored form of the expression. $\newline$ The factored form of $4q^2 - 1$ is $(2q - 1)(2q + 1)$ .