To distribute the expression \((2x + 3)(3x - 1)\), you'll use the distributive property (often called the FOIL method for binomials, which stands for First, Outside, Inside, Last).
Here’s how to distribute:
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First: Multiply the first terms in each binomial: \[ 2x \cdot 3x = 6x^2 \]
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Outside: Multiply the outer terms: \[ 2x \cdot (-1) = -2x \]
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Inside: Multiply the inner terms: \[ 3 \cdot 3x = 9x \]
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Last: Multiply the last terms in each binomial: \[ 3 \cdot (-1) = -3 \]
Now, combine all these results: \[ 6x^2 - 2x + 9x - 3 \]
Combine like terms (\(-2x + 9x\)): \[ 6x^2 + 7x - 3 \]
So, the final result of the distribution of \((2x + 3)(3x - 1)\) is: \[ 6x^2 + 7x - 3 \]
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