To multiply the binomials \((3x + 7)(2x - 5)\) using the FOIL method, we will calculate the product using the following steps:
FOIL stands for First, Outside, Inside, Last.
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First: Multiply the first terms in each binomial. \[ 3x \cdot 2x = 6x^2 \]
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Outside: Multiply the outside terms in the product. \[ 3x \cdot (-5) = -15x \]
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Inside: Multiply the inside terms. \[ 7 \cdot 2x = 14x \]
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Last: Multiply the last terms in each binomial. \[ 7 \cdot (-5) = -35 \]
Now, combine all these results: \[ 6x^2 - 15x + 14x - 35 \]
Combine the like terms \(-15x\) and \(14x\): \[ 6x^2 - 1x - 35 \]
So the answer in the required format is:
Question Blank 1 of 4: \(6\)
Question Blank 2 of 4: \(-1\)
Question Blank 3 of 4: \(x\)
Question Blank 4 of 4: \(-35\)
Final result: \[ 6x^2 - 1x - 35 \]