To verify which expression is equivalent to \((x - 5)(x - 3)\) using the Distributive Property (also known as the FOIL method for binomials), we can expand the expression as follows:
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First: Multiply the first terms: \[ x \cdot x = x^2 \]
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Outer: Multiply the outer terms: \[ x \cdot (-3) = -3x \]
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Inner: Multiply the inner terms: \[ -5 \cdot x = -5x \]
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Last: Multiply the last terms: \[ -5 \cdot (-3) = 15 \]
Now, combine all these results: \[ x^2 - 3x - 5x + 15 \] Combine like terms (\(-3x - 5x\)): \[ x^2 - 8x + 15 \]
Thus, the expression equivalent to \((x - 5)(x - 3)\) is: \[ x^2 - 8x + 15 \]
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