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To factor the expression \( 9x^2 - 1 \), we can recognize it as a difference of squares. The difference of squares formula is: \[ a^2 - b^2 = (a + b)(a - b) \] In this case, \( a^2 = 9x^2 \) and \( b^2 = 1 \). First, identify \( a \) and \( b \): \[ a = 3x \] \[ b = 1 \] Using the difference of squares formula: \[ 9x^2 - 1 = (3x)^2 - 1^2 = (3x + 1)(3x - 1) \] So, the factored form of \( 9x^2 - 1 \) is: \[ (3x + 1)(3x - 1) \]
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