To use the Distributive Property to rewrite the polynomial \((x+8)(x-2)\), we'll apply the distributive property (also known as the FOIL method for binomials).
- First: Multiply the first terms: \(x \cdot x = x^2\).
- Outer: Multiply the outer terms: \(x \cdot (-2) = -2x\).
- Inner: Multiply the inner terms: \(8 \cdot x = 8x\).
- Last: Multiply the last terms: \(8 \cdot (-2) = -16\).
Now, combine these results:
\[ x^2 - 2x + 8x - 16 = x^2 + (8x - 2x) - 16 = x^2 + 6x - 16 \]
Thus, the polynomial rewritten using the Distributive Property is:
\[ x^2 + 6x - 16 \]
In the format requested, the answer is:
- __x^2 + __x + __
- \(1\) (for \(x^2\)), \(6\) (for \(x\)), \(-16\) (the constant term).
So the final answer is: \(1, 6, -16\)
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