To multiply the binomials \( (2x - 5)(x + 7) \), you can use the distributive property (also known as the FOIL method for binomials). Here’s how it works step by step:
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First: Multiply the first terms: \[ 2x \cdot x = 2x^2 \]
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Outer: Multiply the outer terms: \[ 2x \cdot 7 = 14x \]
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Inner: Multiply the inner terms: \[ -5 \cdot x = -5x \]
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Last: Multiply the last terms: \[ -5 \cdot 7 = -35 \]
Now, combine all these results: \[ 2x^2 + 14x - 5x - 35 \]
Next, combine the like terms \( 14x \) and \( -5x \): \[ 2x^2 + (14x - 5x) - 35 = 2x^2 + 9x - 35 \]
Therefore, the product of the binomials \( (2x - 5)(x + 7) \) is: \[ \boxed{2x^2 + 9x - 35} \]
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