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The expanded form of \( (8n - 2)(2n + 3) \) is \( 16n^2 + 20n - 6 \).
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To expand the expression \( (8n-2)(2n+3) \), you can use the distributive property, also known as the FOIL method (First, Outside, Inside, Last). First, you multiply the first terms: \( 8n \cdot 2n = 16n^2 \). Next, multiply the outside terms: \( 8n \cdot 3 = 24n \). Then, multiply the inside terms: \( -2 \cdot 2n = -4n \). Lastly, multiply the last terms: \( -2 \cdot 3 = -6 \). Now, combine the like terms: \[ 16n^2 + 24n - 4n - 6 = 16n^2 + 20n - 6. \] So, the expanded expression is \( 16n^2 + 20n - 6 \).
