To use the Distributive Property (also known as the FOIL method for binomials) to rewrite the polynomial \((x + 8)(x - 2)\), we will multiply each term in the first binomial by each term in the second binomial.
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First, multiply the first terms:
\(x \cdot x = x^2\) -
Next, multiply the outer terms:
\(x \cdot (-2) = -2x\) -
Then, multiply the inner terms:
\(8 \cdot x = 8x\) -
Finally, multiply the last terms:
\(8 \cdot (-2) = -16\)
Now, we combine all these results together:
\[ x^2 - 2x + 8x - 16 \]
Now, combine the like terms \(-2x + 8x\):
\[ x^2 + 6x - 16 \]
So, in the form \(x^2 + __x + __\), we have:
\[ \text{First blank: } 6, \quad \text{Second blank: } -16 \]
Thus, our final answer is: \[ x^2 + 6x - 16 \]
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