To use the Distributive Property (also known as the FOIL method for binomials) to rewrite the polynomial \((x + 8)(x - 2)\), we need to multiply each term in the first binomial by each term in the second binomial.
Here’s the step-by-step calculation:
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First terms: Multiply the first terms in each binomial: \[ x \cdot x = x^2 \]
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Outer terms: Multiply the outer terms: \[ x \cdot (-2) = -2x \]
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Inner terms: Multiply the inner terms: \[ 8 \cdot x = 8x \]
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Last terms: Multiply the last terms in each binomial: \[ 8 \cdot (-2) = -16 \]
Now, we combine all these results: \[ x^2 - 2x + 8x - 16 \]
Next, combine the like terms \(-2x + 8x\): \[ x^2 + 6x - 16 \]
So, the polynomial \((x + 8)(x - 2)\) rewritten using the Distributive Property is: \[ x^2 + 6x - 16 \]
Thus, filling in the blanks as requested: □x² + □x + □ would be:
- \(1\) for the \(x^2\) coefficient
- \(6\) for the \(x\) coefficient
- \(-16\) as the constant term.
So the answer is:
- 1, 6, -16.