To find the complete distribution of the expression \((2x + 3)(3x - 1)\), we will apply the distributive property, also known as the FOIL method (First, Outer, Inner, Last).
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First: Multiply the first terms in each binomial: \[ 2x \cdot 3x = 6x^2 \]
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Outer: Multiply the outer terms: \[ 2x \cdot (-1) = -2x \]
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Inner: Multiply the inner terms: \[ 3 \cdot 3x = 9x \]
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Last: Multiply the last terms: \[ 3 \cdot (-1) = -3 \]
Now, we combine all the results from the above steps: \[ 6x^2 - 2x + 9x - 3 \]
Next, we can combine like terms (the linear terms \(-2x\) and \(9x\)): \[ 6x^2 + 7x - 3 \]
Thus, the complete distribution of \((2x + 3)(3x - 1)\) is: \[ \boxed{6x^2 + 7x - 3} \]