To use the Distributive Property (also known as the FOIL method for binomials) to rewrite the polynomial \((x + 8)(x - 2)\), we multiply each term in the first binomial by each term in the second binomial.
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First, multiply the first terms: \[ x \cdot x = x^2 \]
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Next, multiply the outer terms: \[ x \cdot (-2) = -2x \]
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Then, multiply the inner terms: \[ 8 \cdot x = 8x \]
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Finally, multiply the last terms: \[ 8 \cdot (-2) = -16 \]
Now, combine all these results: \[ x^2 - 2x + 8x - 16 \]
Combine like terms \(-2x\) and \(8x\): \[ x^2 + 6x - 16 \]
So the polynomial \((x + 8)(x - 2)\) expanded using the Distributive Property is: \[ x^2 + 6x - 16 \]