To multiply the binomials \( (2x + 8)(5x - 7) \), we can use the distributive property, often referred to as the FOIL method (First, Outside, Inside, Last).
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First: Multiply the first terms: \[ 2x \cdot 5x = 10x^2 \]
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Outside: Multiply the outer terms: \[ 2x \cdot (-7) = -14x \]
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Inside: Multiply the inner terms: \[ 8 \cdot 5x = 40x \]
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Last: Multiply the last terms: \[ 8 \cdot (-7) = -56 \]
Now, we combine all these results: \[ 10x^2 - 14x + 40x - 56 \]
Combine like terms: \[ 10x^2 + (40x - 14x) - 56 = 10x^2 + 26x - 56 \]
Thus, the product of the binomials \( (2x + 8)(5x - 7) \) is: \[ \boxed{10x^2 + 26x - 56} \]
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