Factor. q^2 - 1 ______

Identify Factoring Technique: Determine the appropriate factoring technique for q^2 - 1. The expression is a difference of squares, which can be factored using the formula a^2 - b^2 = (a - b)(a + b).Identify Squares in Expression: Identify the terms in the expression q^2 - 1 as squares. q^2 is the square of q, and 1 is the square of 1. So we have: q^2 = q * q = (q)^2 1 = 1 * 1 = (1)^2 Therefore, q^2 - 1 can be written as (q)^2 - (1)^2.Apply Difference of Squares Formula: Apply the difference of squares formula to factor q^2 - 1. Using the formula a^2 - b^2 = (a - b)(a + b), we get: (q)^2 - (1)^2 = (q - 1)(q + 1)

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Algebra 1

Factor quadratics: special cases

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Q. Factor.

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q^2 - 1

Identify Factoring Technique: Determine the appropriate factoring technique for $q^2 - 1$ . The expression is a difference of squares, which can be factored using the formula $a^2 - b^2 = (a - b)(a + b)$ .
Identify Squares in Expression: Identify the terms in the expression $q^2 - 1$ as squares. $\newline$ $q^2$ is the square of $q$ , and $1$ is the square of $1$ . So we have: $\newline$ $q^2 = q \times q = (q)^2$ $\newline$ $1 = 1 \times 1 = (1)^2$ $\newline$ Therefore, $q^2 - 1$ can be written as $(q)^2 - (1)^2$ .
Apply Difference of Squares Formula: Apply the difference of squares formula to factor $q^2 - 1$ . Using the formula $a^2 - b^2 = (a - b)(a + b)$ , we get: $(q)^2 - (1)^2 = (q - 1)(q + 1)$