Questions: Find the product. Simplify your answer. (3t-1)(3t+1)

Transcript text: Find the product. Simplify your answer. \[ (3 t-1)(3 t+1) \]

Solution

Step 1: Apply the Difference of Squares Formula

The expression \((3t - 1)(3t + 1)\) is in the form of \((a - b)(a + b)\), which equals \(a^2 - b^2\). Here, \(a = 3t\) and \(b = 1\).

Step 2: Substitute the Values into the Formula

Substitute \(a = 3t\) and \(b = 1\) into the formula: \[ (3t)^2 - (1)^2 \]

Step 3: Simplify the Expression

Calculate \((3t)^2\) and \((1)^2\): \[ 9t^2 - 1 \]

The simplified form of the product is \(9t^2 - 1\).

\(\boxed{9t^2 - 1}\)

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