To correctly distribute the expression \((2x + 3)(3x - 1)\), we need to apply the distributive property (also known as the FOIL method for binomials).
Here's the step-by-step distribution:
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First: Multiply the first terms: \[ 2x \cdot 3x = 6x^2 \]
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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 these results: \[ 6x^2 - 2x + 9x - 3 \]
Combining like terms (\(-2x + 9x\)): \[ 6x^2 + 7x - 3 \]
Based on your options, the correct and complete distribution should yield \(6x^2 + 7x - 3\), which looks somewhat like the original expressions you provided. However, none of your answer lines exactly match this result in full. Make sure to check if one of the options is a rearrangement or partial result, as sometimes there are notation differences in how the expressions are written.
If you need help clarifying an option you provided, you can write them again clearly, and I'll assist you in identifying the correct choice based on the mathematical expansion above.